I actually just picked up one of those little galaxian sized cabs that is white right now, but the laminate on it currently is really crappy. It is made from particle board, so painting is out of the question. I am thinking of relaminating it in white, but I really want to find some high gloss white, give it an i-arcade(apple) look.
There is really no reason you can't do it in white, but it will take more time as you will have to protect it some more.
As for authentic, doing it in white will have no effect. If has the right shape, a good control panel, and good marquee/control panel artwork, white won't matter.