When you run a PS1 game through Adrenaline, it hooks onto the Vita's official PS1 emulator. So when you press and hold the PS Button, then choose "Settings -> Open Official Settings", you will encounter the official PS1 emulator settings as if it was a legit PS1 game.
So from there, like any other legit PS1 game on the Vita, you can just map L2/R2/L3/R3 to the rear touch pad via the controller settings. So yes, you can 'emulate' the triggers and stick buttons as well.