Hmmm... couldn’t every law signed, every executive order given during his term be challenged as illegitimate?
Absolutely! And with good reason. And a very likely outcome of everything he did being declared unconstitutional!............
Nah. The republican controlled congress would pass a bill stating obama “didn’t really know he wasn’t American” so he can’t be charged. And the republican president would sign it. Or, to hell with congress. The republican president could just sign an executive order.