The farthest Quarian criminal activity I can see is someone like Xen, trying to Hack the Geth to enslave them for the Quarians. Again a crime for greater good of their people. A thief serves only himself, or those extremelly close to him.
It might be a personal preference though. I disliked Kasumi, and I dislike thieves. More so than murderers and other criminals.
In case of galactic evacuation, such people wouldnt be brought. They are self serving and will ultimately serve none but themselves and that is a risk that cant be taken, when a tiny thing can mean the difference between survival and extinction.
It depends on how they end up presenting the voyage to Andromeda. If they're putting everyone in suspended animation, so the people who arrive in Andromeda are the same people who left the Milky Way, then yeah, there's a good argument for whoever controlled the ARKCON project - the Council, I would guess - having had stringent screening measures in place that would've kept out all but the very best - that is to say, sneakiest - criminals. (Well, them and those rich enough to just buy themselves a place with resources or what have you.)
If it's a generation ship, on the other hand, then there's really no way of telling what kind of people we'll have with us when we arrive in Andromeda, since they'll all - barring the Asari and Krogan - have been born on the ship.
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A huge amount of money, time and resources is required to bring about an armada of colony ships or even a few massive ones. From the trilogy, Quarians lived in dilapidated ships. They really were the equivalent of the European Gypsies.
Any Quarian in Andromeda is a gift from the Alliance.
Well, that's my view.
I dunno, man--if you're building an intergalactic colony ship, that'll have to fly further and for longer than any ship that's come before, I'd say you'd probably be remiss not to seek the expertise of the galaxy's foremost authority on long-duration space flight. No matter how ramshackle their ships might have been, it's hard to imagine that the Quarians didn't learn a great deal about what it takes to keep spacecraft going with limited support and resources over the course of their hundreds of years of exile. At the very least, it'd be an easy way to justify their being on the ship for the writers, and I get the impression BioWare want to salvage as much from the Milky Way as they can.
OP Response:
I'd be deeply, deeply sad if we didn't have a new Quarian squadmate, but I haven't really put much thought into exactly what kind of character I'd want them to be. I like the idea of a Kasumi-esque thief/hacker; I liked her, and wish she'd gotten more to do in the old games.
I will say that I'd want the new character to be at least somewhat self-serving, though--we've yet to come across a Quarian who didn't always put the Fleet first - which is justified, considering their culture, but there's always an exception - and I think it'd make for a nice contrast. There'd be more to them, of course, but some aspect of at least surface-level selfishness would be oddly refreshing.