Actually, with 23 seconds to go, and leading by two, I think the other team would try to foul you as quickly as possible, get you to the line, hope you make 1-2, and go for a three to tie the game. Even more so if they're down by one. They're certainly not going to let you run down the shot clock.
This is the behavior I've seen most often with the end-game.
Also, a player's Experience will help determine how he plays, and this is particularly noticeable with the shot selection at the end of the game.