Personally, a Mary Sue/Gary Stu is, yeah, a poorly developed character who gets everything handed to him/her without actually earning anything and, in some cases, someone who has all the answers and/or is incredibly powerful without having actually earned that power.
I feel like Inquisition's plot steers The Inquisitor in some of those directions, as i said. A guy who knows nothing about anything gets handed to him from day 1 the keys of a powerful organization because his hand glows green, plus everyone bows to his judgment from the get-go
You're confusing two things - Inquisitor only got "handed" things in a sense that they had all this new responsibility and role thrown on them and they suddenly have to find themselves in a new situation, thought by many people to be savior of the world. Whether they grow into the role, or a role of capable leader, is pretty much entirely dependent on how you play them.
Honestly, my favorite part about Dragon Age:Origins is, well, Dragon Age:Awakening because throughout all of that expansion it was made clear that The Warden had stopped being the "underdog" and had become the big guy, the one to fear, and the awesome part is that he had earned it. The Warden, i feel like, becomes better and better as the game and the plot advances.
The Inquisitor, IMHO, starts awesome, becomes even more awesome and kills the (quite weak) villain with awesome. I never felt like he had actually earned power(pun intended) throughout his journey and, honestly, i like Solas' part in Trespasser mostly because all of that power, in the end, means nothing, just as it should
Funny that you say that, because I think Warden is way more Sue'ish than the Inquisitor. Ever since the origin stories the game keeps underlining how awesome they are - that's a pretty telltale sign of Mary Sue. Inquisition in that regard is more balanced - as much of the potential they could have, DAI makes it pretty clear that the greatness is imposed on the PC, rather than it's sort of inherent, like in case of the Warden. And a lot more depends on Inquisitor actually going out there and taking care of their image by doing stuff in order to actually make Inquisition grow beyond bare minimum. We don't have much of that in DAO.
There are also a lot of moments in DAO where the resolution hinges on a fact that Warden Is Awesome or has a copious amounts of sheer luck.
Ostagar gets attacked, everybody dies around you? Don't worry, the ancient witch will swoop down and save specifically you. She'll also hand you papers that will make creation of the army possible - yes, you'd have to work for it, but the road to getting this alliance is clear, as evidenced by the fact that Loghain's people can't do anything to be let into Orzammar, while HoF just approaches the guards and flashes the treaties, like a diamond-studded credit card before a very expensive club.
Branca couldn't get to the Anvil in what... 2 years time and resorted to turning some of her people into Broodmothers? Warden just breezes through that place with nothing but their little team. They get locked in the Fade, even those who are entirely unfamiliar with it? THEY'RE the only ones who can help everyone get away from it. Not even Wynne or Morrigan, who realistically should know much more about the Fade, do much to help there, if at all.
And so on and so forth.