(preferably with something hardcore like Kilz since a SNES is all slick and shiny and textured)
No! Kilz is sheetrock and drywall primer. It's weak in comparison to correct primers on any other surfaces. I've seen Kilz scratch off plastic just as easily as other paints (I've cap sprayed (HVLP) many a light rings, vents, canisters, etc for custom homes). Also, Kilz almost always leaves a rough finish and often spits.
Denatured Alcohol is best to clean the system down with, then do a *quick* wipe with lacquer thinner to break the surface - not too much/too long or you'll dissolve the plastic. The plastic/dye automotive interior paint I referred to early is really tough and has a nice fine spray fan, but it's limited in colors and needs to be put on in multiple coats (3 light coats and a solid top coat). I have some "aircraft" paint that would really take a beating, but that stuff is really nasty to work with (and requires $1200 minimum setup/rig to spray).