With Chapters 55-56, I have some theories regarding Quirrell's true plan. He is Voldemort (or rather contains a piece of Voldemort) but we know he doesn't want Harry dead; he's had ample opportunity to simply murder Harry if that was the goal. I think rescuing Bellatrix is a distraction as well, really nothing more than a cover story or "fortunate side effect" of achieving the true goal. If rescuing Bellatrix was the true goal, he wouldn't have jeopardized the mission by attempting to murder the auror.

I think Quirrell's ultimate goal is the Dementation of Harry, probably in order to draw out Harry's dark side (which I think is the horcrux-fragment of Voldemort). He tried this at Hogwarts and it would have worked if not for Hermione's intervention. Since he was unlikely to be able to bring Dementors to Hogwarts a second time, he concluded that he'd have to bring Harry to Azkaban. The rescue plan is a cover story designed to persuade Harry into going to Azkaban--although I suppose Quirrell figured he might as well make the rescue target someone who could actually be useful to him/Voldemort if freed.

So basically Quirrell deliberately put himself out of commission, thinking that Harry would quickly fall prey to the Dementors in such a situation. The hole in my theory is that this seems like an all-or-nothing play: he's now revealed at least three pieces of important information to Harry (1. His own willingness to kill innocents; 2. The spell-clash aspect of their joined magics--which for my theory to be correct, Quirrell must already have known about; and 3. Quirrell's own insanely-high power level). These three pieces together are probably enough to make Harry suspect that Quirrell is an aspect of Voldemort, once he has the chance to think things through. Quirrell is subtle enough that he should have had a backup plan in place in order to retain Harry's trust in the event that Harry is not Demented, but I can't imagine what that might be. Maybe Quirrell's backup plan involves the Imperius Curse or memory charms or something. I'd say that "Kill Harry" would be the simplest and most obvious backup plan, but I think Voldemort wants/needs Harry alive.

Not a prediction so much as a guess: Bellatrix's Innervate charm did work on Quirrell. He's currently faking unconsciousness (and remaining in the form that gives himself some protection from the Dementors) as he waits to see whether Harry will or will not succumb to Dementation.