Do quick games help improve your knowledge?


No I don't think blitz games will improve you're opening knowledge. They're just to darn fast to get anything useful out of them. You're much better off playing correspondence ESPECIALLY if you want to form a solid understanding of openings.

I think blitz games can be helpful, if that's what you're looking for. For example, they're a very good way to get a feel for how a specific opening operates...you won't learn deep theory this way, but you may get a sense about some of the strategic themes.
I often go through and analyze my blitz games looking for turning points; and more often than not, I find interesting positions to study. Just yesterday I blew a promising 5/0 game here on Live Chess first by giving up on a strong attack because I couldn't find the kill move:
Here 1...Ndc5! wins; but having spent about 45 seconds looking I'd found nothing, so I panicked and played 1...Qxc2+ hoping that the exposed king and general damage would pay off later. So this proved to be a good tactical exercise--but only if I'd spent the time to review it afterward.
Later in the same game I had another opportunity to win, but I'd blown so much time on the clock I didn't see that either. But going back over the game, I found the position very interesting:
White just played 1 Kc3, which loses to 1...Kh5. After that move, I'd have had enough time to eliminate the opposition and get my g-pawn rolling before white dismantled my queenside triad. Instead, I played 1...Kf5--here the mistake is that I left white's kingside pawns unfought and in my rear. In trying to maintain the balance on both fronts, I lost the whole shooting-match. (Incidentally, if instead of 1 Kc3 white had played 1 g4, I would have been completely lost--there would have been no easy way for me to approach white's kingside pawns.)
So this is how I try to use blitz games to my benefit. Certainly, not all blitz games will be helpful; but reflection and analysis on the most interesting positions can't help but improve all aspects of your play.