Sure, you can basicly color them in any way you want. You should know that you will have a hard time getting them completly white when they are orange. I havent tried white yet, but I would assume they will have an orange glare to them, since the base color is orange.
Red should be no problem since it is so close to orange in the colorscheme.
Black should still be the easiest. Just leave the goggles in longer if you want to make sure they become completly black. If they aren't as black as you wanted, just give them another round.
As far as spray painting goes, well I don't see a reason not to. The paint won't stick in the same way though and will slowly chip away when used. Remember to cover up the foam when spray painting though, otherwise your goggles will be ruined.