After a correspondence game is finished and the new ratings are calculated, are the ratings prior to the match started used in the calculation or are the current ratings used (games might have finished after the game in question started, changing the players' ratings)?

I don't know for sure but I was wondering the same thing.  For what it's worth, I'm in a game now with someone that was rated upper 1400's when we started.  If I lost it said that I would lose over 100 rating points.  We are about 14 moves in and he has won 4 games since we started, and is now rated mid 1700's.  After we started the game I checked his profile and saw that he is FIDE rated 2258 and way out of my league, but I was happy to see that if I lose now I only lose 44 ratings points, so apparently the current rating is what matters and not the rating at the start of the game.