I would conjecture NO. The Supreme Court has yet to decide a case of contested citizenship for a Presidential candidate.
This leaves only supposition, but the following Congressional Research Service report suggests only that eligble candidates meet legal requirements of citizenship "at birth".
[NOTE: link is to a pdf derived via wikipedia article on the "Natural-born-citizen clause"].
The weight of legal and historical authority indicates that the term "natural born" citizen would mean a person who is entitled to U.S. citizenship "by birth" or "at birth", either by being born "in" the United States and under its jurisdiction, even those born to alien parents; by being born abroad to U.S. citizen-parents; or by being born in other situations meeting legal requirements for U.S. citizenship "at birth". Such term, however, would not include a person who was not a U.S. citizen by birth or at birth, and who was thus born an "alien" required to go through the legal process of "naturalization" to become a U.S. citizen.
A relevant passage from the document (pg.28):
have no law, (as the French have,) to decitizenize a citizen who has become such either by the natural process of birth, or by the legal process of adoption.... The Constitution itself does not make the citizens; it is, in fact, made by them. It only intends and recognizes such of them as are natural—home-born; and provides for the naturalization of such of them as were alien—foreign born ....
[UPDATE] I add this scenario as a nightmare question for benefit of DJClayworth, who commented below. If a foreign surrogate were to deliver in an American medical facility abroad for American citizen parents, undoubtedly yes, but what if delivered elsewhere? The document referenced uses this "reasoning":
...could develop the requisite allegiances and reverences for the United States passed down, inculcated, and taught by one’s parent-citizens, and would have a lifetime of allegiance to the United States at least as strong, in a theoretical sense, as one of a “native born” citizen.
So, could we treat a child of a foreign surrogate, delivered with the express intention of adoption by American citizens, as native-born if not delivered in an American medical facility?