Yes, in Miami in 1971.
That makes him NATIVE born but not NATURAL Born.
http://www.birthers.org/USC/Vattel.html
That site covers NBC as it was understood to the founders. The concept of birth within the country to two citizen parents was so widely understood by people with knowledge of international law in 1787 that the text of the Constitution was very brief on the subject. Vattel was the acknowledged authority.
SCOTUS has dealt with citizenship and native born citizenship but it has never dealt with NBC. The old sources remain the best.
I would think he would be eligible.