I would tell you yes, it can.
Conscription has been a historic norm for maintaining military forces, long before national security systems and the what not were around to reliably track and reclaim deserters. For most of history, and in most places in the world today, this is true- if you really want to run away from the government/military/whoever, you can. It's just a matter of how difficult you're willing to make it for anyone else to follow, and how much they care. Even in non-conscript security forces, such as the Afghan or Iraqi security forces during the American occupations, desertion rates were nothing to sneeze at- and I'm not talking about the mass-abandonment during the ISIS expansion either.
The biggest obstacle to dessertion often isn't the ability of the organization to pursue- it's the willingness of the desertee to do it. The reason most desertions fail is because people go back home, or stay in the area, or otherwise make it easy to be found. On the other hand, if someone has a good support network willing to hide them, be it friends or family or tribve, pursuit is often difficult or effectively impossible. And that's on home ground- populations normally friendly to the organization.
What prevents desertion from normally destroying organizations isn't the difficulty of deserting (which is feasible) or the punishments for trying (which are - it's the general unwillingness of people to do so, for reasons other than 'sticks.' The biggest of which is the lack of perceived alternatives- even if a reluctant Warden wants to flee, they still have the taint, they still have the whispers, and they still have the Calling. If your name isn't Fiona, there's no alternative community to that- you either share that exclusive burden with the Wardens, are none at all.
That the Wardens have an international presence, and a ping-detector if they're near you? That's just an added bonus to the difficulty and the perceived lack of chances. But the real deterance to crippling desertion isn't that people can't- it's that most people don't (want to).
None of that is particularly compelling.
Conscription actually
isn't a historic norm; apart from short-term levies for specific tasks (i.e. temporary local defense against an invader) mass conscription was seen as counterproductive, harmful to the national economy, and difficult to control. You couldn't really use levied civilians in melee combat, because they wouldn't know what to do and it was fundamentally more difficult to train than the later use of firearms; levied groups would have to be those already used to the employment of weapons, such as hunters, and those aren't exactly large groups in the first place, and there were usually specific non-random legal obligations for them to do so in the first place. Organizations that employed the less-than-willing, such as the Royal Navy or the Frederician Prussian army, had to also make use of the aforementioned horrific disciplinary action in order to keep men in line. They also, y'know, paid wages. And they still suffered tremendous desertion rates. Mass Royal Navy desertion actually helped start a war once upon a time.
In fact, what Blackwall shows us in
Inquisition, with the Hinterlands farmers, looks much more like the sort of "conscription" you might find in militaries before the early modern period: temporary service in a role that was militarily worthless apart from as a distraction, like the French
arièrre-ban. There would be no reasonable expectation of being able to keep conscripted men in the field for any appreciable amount of time. Kingdoms simply didn't have the organization to keep track of them all, or hunt them down when they ran off.
Famously, this changed in 1793 with Republican France's proclamation of the
levée en masse, which raised the first conscript army in world history. France, however, had begun to develop the sort of bureaucratic machinery capable of keeping most of its conscripts in line. Its troops were compensated, after a fashion. And it still fell abysmally short of its target manpower; supposedly the entire able-bodied manpower of France was subject to conscription, but in practice only about 800,000 individuals were conscripted, and of
those less than half actually ended up serving for any appreciable length of time because the authorities simply couldn't keep track of everybody who deserted. It took five years to finally figure out
how to take these mass armies in (the promulgation of the
loi Jourdan), and several more for the vast new French state to try to manage it effectively.
Many subsequent attempts at general conscription did not do significantly better for some time. The slaveholder rebellion in the American South lacked a real bureaucracy from the start, and had to create a provost system on the fly, with the result that the entire Confederate army deserted
multiple times over throughout the course of the war. Every spring, before campaigning season, rebel armies would have to almost entirely reconstitute themselves. It was an utter mess. Federal armies, which retained their military support system and modern bureaucracy, and which had a much better-run provost system, did better at retaining their troops, but still suffered severe desertion problems, along with the 'skulking' phenomenon where soldiers would hide during battles to try to take advantage of the confusion, then rejoin their units later.
Sustainable conscript armies are simply an outrageous anachronism in this context.
Desertion for many of these men was not nearly as impossible as you seem to be making it out. For one thing, they had a very strong alternative to fighting: they didn't want to die. And they knew that they would almost certainly not get caught if they ran. They were only rarely kept track of in civilian life, if at all, and almost never kept track of in military life. They were not psychologically and ideologically indoctrinated like modern recruits are; they were not trained to believe that they could survive if they were sufficiently skilled. They did not have a support system in place, true, but frankly neither did any of the militaries, most of which were fairly rudimentarily organized. Even the ramshackle Iraqi or Afghan states, for all their problems, possess far greater capacity to control, track, and train their soldiers than any medieval entity.
None of this means that the Wardens would not have any troops at all. Obviously they would. But it's hard for me to believe that uncompensated conscripts, many of whom were previously criminals, wouldn't leave by the scores. If, under these circumstances, the Wardens retained even a quarter of the people they originally conscripted, I would be shocked.
However, since the Warden organization
is obviously sustainable, I don't think that this happens. See below.
As for why the Wardens still exist as an institution- that one is easier. Because Darkspawn are still an issue, even outside of the Blights, which justifies noble and national support to Wardens even outside of crisis times. Because the Wardens have secured a power base in the Anderfels, from which they can support and subsidize Wardens elsewhere. Because the Wardens have broad social legetimacy and are generally seen as non-threatening, which maintains public support and avoids political controversy (however imperfectly). Presumably because the Wardens do a little someone extra on the side for money and influence, such as Deep Roads expeditions or clearing Darkspawn surface raids or selling/trading recovered artifacts or leveraging the connections of their higher-ranked recruits (disgraced nobility or seventh sons or relations of merchants) to their advantage.
And, of course, because Bioware intended them to. But that doesn't need to be the only one.
Oh, come on, you know that most of that stuff isn't what I was pointing at. You're talking about reasons why people wouldn't actively try to get rid of the Wardens; I'm talking about the fact that Wardens need something to
actively support them, which is another matter entirely. Their legitimacy isn't relevant, and neither is their military justification. They simply need somebody to pay for it all. There's a vast gulf between "the Wardens are nice to have around, especially when darkspawn are about, and they seem like all right people" and "here Wardens have a bunch of money to defray the operational costs of your private army".
I pointed out that the way for comparable medieval organizations, the crusading orders, to generate money enough to run was to be granted revenues by crowns, often through gaining a usufruct for certain estates. This made them political players in various kingdoms, and sometimes made them independent powers of their own (the Knights of St. John in Rhodes and Malta; the German Order in Transylvania, Prussia, and Livonia). (Now, to be fair, the military orders also needed these estates to generate things like food, which as we all know BioWare writers don't really notice and/or care about, especially in a military context. But since Thedas' economy is so highly monetized, and because harping on the food thing yet again would be trite, I'll just assume that all they need is revenue flow and go from there.) These are the exact things that the Wardens claim to be against, although it's embarrassingly easy to point out that they more or less run the Anderfels. It is a stupid tenet of the Order, and it is manifestly unreasonable, and it seemingly exists only for Riordan to tut-tut at the Hero and Alistair while tacitly approving of their actions anyway so that the Hero seems like more of a renegade because BioWare writing often fetishizes "acting like a renegade despite all evidence to the contrary".
Weisshaupt could theoretically help. But the games have repeatedly shown that Weisshaupt doesn't actually get involved in anything down south. The only assistance you see from Weisshaupt in
Awakening, for instance, is Mistress Woolsey; almost all actual aid is provided by the Grey Wardens of Orlais, which just redistributes the "where is the money coming from" to Orlais instead of Ferelden while not actually solving the problem. In later sources, Weisshaupt shows that it's so completely disconnected from southern Thedas that it can lose contact with subordinate organizations for several months to a year. That is not the sort of organization that provides effective support. You'd think that maintaining communications would be a little bit easier than making payroll. So while that
might solve the problem, I don't think that the games and books as written actually
allow it to.
My point was that either the Grey Warden tenet of nonintervention is complete nonsense and the Wardens own estates (or estate revenues) anyway, thus giving them the regular funds that they need to actually maintain an organization, or they don't have an organization. Since they obviously
do have an organization, the Wardens must possess those estates; since they obviously do
not have insane desertion rates, the Wardens must possess estate revenues in sufficient quantity to actually be able to compensate their troops, and give them more of a motivation to turn into ghouls and fight monsters than just "well,
somebody has to think they're saving the world".