As far as I know, yes! The rating changes are related to the ratings of the two opponents the exact moment the game finishes!They have nothing to do with the ratings at the beginning of the game.
However, it is possible that you will get the same points for the win as it can happen, for exampe if you win, a player with rating 1200 and one with 1195! You might take, in both cases, +13!
I hope my explanation was good!
I was wondering that , if you playing someone with a 1200 rating and you were going to get +13 for a win - if in the time it takes to finish the game the 1200 rated opponent loses a game and his rating drops, do you get less points for a win?