$20 HU SNG, huge debate with friend

[ukdentisto32]

Ok, I dont play $22 SNG, i play much higher, but my friend who is learning heads up play just started and i was watching him play the other day and this hand came up. Sorry, no converter.

Full Tilt Poker HU SNG Turbo
Hero - 780 chips
Villain - 2220 chips

Villain is actually a descent player, only real weeakness that can be spotted quickly is that he is very passive, calling MANY hands but raising not nearly enough. Hero is very aggressive, raising every other pot and cbetting most of the time, giving up on turn if cbet gets called. He is down to 780 chips just by raising, betting and 2 barreling and missing flops. Anyways, to the hand.

Hero raises to 120 with A9 off, villain calls. Pot is 240. Flop is a rainbow QT3, hero is first to act and shoves all in.

I argue that regardless of whether he folds or not, this is a bad play. My friend argues that it is not a good play but is a descent play (profitable or better).

Is it a bad play, or not?