It depends on the game, but you will probably be okay. Some old boards, like the Williams, are pretty sensitive to low voltage. And since you have to send the +5V to about 4 different boards with those, the +5v can dip a bit.
I haven't had a problem running native jamma boards with a pc power supply, but the only way you will know for sure is to try. If the voltage is too low, the game will probably just do flakey things like reset while playing and stuff like that.