Yes "Dragonball Z: Budokai Tenkaichi 3" will work on a compatible PS3.
Only the launch PS3s (20 and 60 gb) and the 80 gb that came bundled with Motorstorm and later Metal Gear Solid can play PS2 games.
Backward compatible PS3 models will have 4 USB ports and have one of the following model numbers: CECHE 80 gig, CECHA 60 gig, CECHB 20 gig. Any newer PS3s or slim PS3 cannot play PS2 games.
Compatibility list: http://tinyurl.com/9sncqtz