I haven't tried this in a few months, but I don't think PCSX has been updated since, so I assume it still holds true.
I tried playing Castlevania SOTN on PCSX with a few GameShark codes enabled. I was using the built-in cheat menu, and put in the typical infinite health code. After starting the game, I noticed the code wasn't working. I tried a few other codes, and it was the same result.
The same thing happened with Final Fantasy Tactics. I entered infinite health codes for each player team slot, and none of the codes worked. All my allies still took damage.
There are a few codes that actually did work, but most didn't appear to. Does PCSX not fully support GameShark? Should I try running an actual GameShark before the game?