It seems that this is a quantitative question. i've wondered about it before, so I did the math for the flop... I hope.

p(specific two suited, when 3 of same are on the flop) =0.06 per person
p(no flush per person) = 0.9538
opponents = 7
p(no flush at table)= 0.72 (this is a suprise to me)

EV

You make full/quads: 0.22 x 1 (fraction you win)
You are unimproved: 0.78 x 0.37 (fraction you win when your opponent doesn't have, or make, a flush; =1-(0.28 (has flush) + 0.35 (makes flush)

EV = 0.51

So, given overlay the flop must be played. I have no idea how often villian folds to a push here. Maybe someone who is mathy can take this further to argue an optimal play?