When a game is cut short and the winner is determined by material, do points still count if they're from promoted pawns? At my school, we play with a time limit, and the winner is decided based on points (for example, a pawn is 1, a rook 5, a knight 3).

Let's say my queen is taken by my opponent, scoring 9 points. If I get my pawn to the other end and exchange it for a queen, do they lose those points?
Points in chess mean nothing with respect to the actual play of the game with regards to the rules. They are only a reference to give players a general sense of what value each piece has relative to the next piece.

In essence, if you lose your queen, 9 points, but promote a pawn, you gain 9 points minus one for the pawn, so you would still be down one in material, but again, that is just a relative reference to give you an idea where you stand.

These relative point values are estimates, and depending on who you talk to, they may vary. Here is a list of various values that strong players have assigned over the years here. Bobby Fischer said that the bishop was worth 3.25 because he loved bishops.