Well, not precisely. They can use a firearm to do it, but doing so may open them up to other charges, as pointed out.Does a convicted felon or other disqualified person lose the right to defend themselves? No, but they can't use a firearm to do it.
So a drunk person (or convicted felon) who killed someone with a firearm in self-defense might not be convicted of murder if the circumstances were extremely clearcut in his favor. But he might still be prosecuted for possessing the firearm and (in the case of the intoxicated individual) might lose the right to carry, or even to own, firearms in the future.