Is it OK to re-paint a gas-range grill with paint?
Given the direct flame exposure, and that the flames are actually quite a bit hotter than BBQ paint is rated for (1950C for natural gas, 2392C for propane) I'd suggest sticking to clean, coat with vegetable oil (wipe on a thin layer) and bake. This makes a pretty good finish, and does not involve anything that's not going to happen in normal food preparation as far as "what might burn off." 

Wikipedia on flame temperatures. These are probably a touch high for "in practice", but given that they are also in Celsius, and the grill paint is rated in Farenheit, I'll stick with "grill paint will burn off."