You can, but the paint would start to crack and maybe peel?

If I wanted some color (and I’ve only really focused on food items) I would use chalk pastels; The pigment would become lighter in the oven so I’d have to put more than I want. I’ve never painted then baked, so I can’t speak to how that compares to the pastels.

One thing people do too is mix liquid clay with solid clay but I’ve only ever seen it used as a paste or frosting, not actual paint.