If we followed precedent and the body of laws, yes. But SCOTUS has become politicized and will rule in Cruz's favor. The Tribe/Olson opinion on McCain contained a gratuitous finding on Obama finding him eligible since he was born in Hawaii, a natural born citizen via jus solis. Cruz will be found as natural born thru jus sanguinis even though one of his parents was not a US citizen. Everyone seems to forget the controversy over Chester A. Arthur.
I agree Obama should be in jail, especially due to his fraudulent long form BC, which Trump forced him into releasing.
Except for the part where they can't prove it, and no hospital takes credit for it. In fact Hawaii isn't exactly naming everything after him.