I suppose you could, I've never heard of anyone doing this though. The paint is likely just going to bubble up in time from the heat and end up looking worse than it did before you painted it.
Not a paint expert, but most microwaves are just painted with a normal white enamel paint. Not knowing what you have I'd just say avoid getting into any vent holes on the inside, you don't want to paint over the antenna thats likely to be located behind one of these vent holes if your using spray paint.
Don't use any type of metalic paint, like chrome or metal flake or anything like that.
Food is likely to taste like burning over heated paint as well for a while afterwards. | 
White Wine 
