Patching that is possible I guess, but it would also require setting up some sort of calibration in the game.
So apparently, to make pressure sensitive PS2 controller work in PCSX2, you need ShanWan PS2-to-PS3 adapter (or equivalent), DSHidMini, and set input mode to SDL. Since I lack both pieces of hardware, I can't test it myself. Or skip the middleman and get a PS3 controller, which is a better option anyway for several reasons.