Interesting…I've been tempted to introduce my roommate to the 2 player variant, but I think the general assumption around here has been that it's probably only barely playable.
The expansions should work, on the whole. You won't be able to use the Cylon Leaders from Pegasus, but no big loss there. And Conflicted Loyalties from the Exodus expansion might be a little tricky; it includes both Final Five cards (these hurt you for looking at another player's loyalty card, which should be interesting, assuming Baltar's ability (for example) comes up much in your games), and Personal Goals (which lose a resource at the end of the game if you haven't met a given condition; the problem is that when you do succeed at a goal, you draw a new loyalty card to replace it, so you might want to skip that part, or just leave these cards out).
Likewise, the alternate endgames from each expansion should only present minor problems. There's a known exploit or two in the New Caprica ending from Pegasus, which would probably be even more severe with two players, but it shouldn't be hard to come to an understanding about that. The Ionian Nebula from Exodus might actually be better with only two players, though you might want to play without the "Strange Music" card.