AQs UTG, makes TP on a board with draws

Do people really see situations in which hero's turn fold is a bad play? Granted, we don't have good numbers, but we've got a guy who suffered through a 3 bet flop, and he's going to lead the turn certainly knowing that somebody's calling him down based on previous action.

How often does this guy NOT have a flush?

(Granted, he could have 2 pair or a set, but I don't think I'd want to bet on it...