Although I did not get around to testing this today, I am told by my workmates (I work in an electronics workshop) that PS2 will have no problem running off even the crappiest cheap inverter. Also note that the mini version of the PS2 runs off 12 volts anyway, so you could connect this directly to the battery if you wish.
There would be a small risk that when the car was running (and the electrical system jumps to about 13.8 volts) it would be too much for the PS2 and damage it, but I'd say this is extremely unlikely.
Anyway, in answer to your question, it will run fine on a modified square wave inverter