Generic PS2-to-USB adapters ignore that part of the spec, so the PC doesn't receive these inputs at all. You'd need to build your own adapter out of Arduino or something.
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.