No, and the way he talks about Cuba, there would clearly be a loyalty conflict.
“It is an established maxim, received by all political writers that every person owes a natural allegiance to the government of that country in which he is born. Allegiance is defined to be a tie, that binds the subject to the state, and in consequence of his obedience, he is entitled to protection… The children of aliens, born in this state, are considered as natural born subjects, and have the same rights with the rest of the citizens.”
Zephaniah Swift, A system of the laws of the state of Connecticut: in six books, Volumes 1-2 of A System of the Laws of the State of Connecticut: pg. 163,167 (1795)
http://press-pubs.uchicago.edu/founders/documents/a1_2_2s6.html
The following is an enormous list of legal citations, from Obama operatives, but you need to know what you are up against:
http://nativeborncitizen.wordpress.com/natural-born-quotes/
James Madison, The Founders’ Constitution Volume 2, Article 1, Section 2, Clause 2,
Madison:
It is an established maxim that birth is a criterion of allegiance. Birth however derives its force sometimes from place and sometimes from parentage, but in general place is the most certain criterion; it is what applies in the United States; it will therefore be unnecessary to investigate any other.
http://www.scribd.com/doc/79655719/James-Madison-on-Contested-Election-Citizenship-And-Birthright-22-May-1789-House-of-Representatives