The answer is, as with most things in poker, it depends. Mostly it depends on the texture of the board and the range of hands that your opponent is betting. With suited run-downs you are really hoping to flop a straight/straight draw and have the flush outs as back-up. The flush outs allow you to build a large pot and force out better flush draws, etc. The flush outs also give you an exceptional equity edge in the case where two people both flop the nut straight, but one is free-rolling the other with the flush redraw.

If you don't have straight outs, then chasing a Q high or J high flush is certainly going to be -EV. If you hold Qd-Jd-10c-9c on a board that is 8d-4d-3c, your hand most likely belongs in the muck after the flop. Even if you see the turn for free and it completes the flush, you still aren't in a position to bet or call a bet.

Also, many times with such run-down hands, you will flop a draw on a rainbow board. If there is action on the flop and the turn brings a flush draw along with your straight draw, most of the time you will be able to count the cards completing the flush as outs.