Not according to the US State Department Foreign Affairs Manual:
7 FAM 1131.6 Nature of Citizenship Acquired by Birth Abroad to U.S. Citizen Parents
7 FAM 1131.6-1 Status Generally (TL:CON-68; 04-01-1998)
Persons born abroad who acquire U.S. citizenship at birth by statute generally have the same rights and are subject to the same obligations as citizens born in the United States who acquire citizenship pursuant to the 14th Amendment to the Constitution. One exception is that they may be subject to citizenship retention requirements.
7 FAM 1131.6-2 Eligibility for Presidency (TL:CON-68; 04-01-1998).
It has never been determined definitively by a court whether a person who acquired U.S. citizenship by birth abroad to U.S. citizens is a naturalborn citizen within the meaning of Article II of the Constitution and, therefore, eligible for the Presidency.
b. Section 1, Article II, of the Constitution states, in relevant part that “No Person except a natural born Citizen...shall be eligible for the Office of President;”
c. The Constitution does not define "natural born". The “Act to establish an Uniform Rule of Naturalization”, enacted March 26, 1790, (1 Stat. 103,104) provided that, “...the children of citizens of the United States, that may be born ... out of the limits of the United States, shall be considered as natural born citizens: Provided that the right of citizenship shall not descend to persons whose fathers have never been resident in the United States.”
7 FAM 1130 Page 8 of 103
U.S. Department of State Foreign Affairs Manual Volume 7 - Consular Affairs
7 FAM 1130 Page 9 of 103
d. This statute is no longer operative, however, and its formula is not included in modern nationality statutes. In any event, the fact that someone is a natural born citizen pursuant to a statute does not necessarily imply that he or she is such a citizen for Constitutional purposes.
7 FAM 1131.6-3 Not Citizens by “Naturalization” (TL:CON-68; 04-01-1998) Section 201(g) NA and section 301(g) INA (formerly section 301(a)(7) INA) both specify that naturalization is "the conferring of nationality of a state upon a person after birth." Clearly, then, Americans who acquired their citizenship by birth abroad to U.S. citizens are not considered naturalized citizens under either act.
7 FAM 1130 Page 9 of 103
The Constitution identifies only two types of citizen, naturalized or natural born. If you were born a citizen you are natural born. If you became a citizen at some point after birth, you a a naturalized citizen. There is plenty of precedent - John McCain, George Romney, millions of children born to servicemen stationed overseas. Are you prepared to claim that a child of an illegal immigrant that just happened to have been smuggled across the border in its mother's womb the day before being born CAN become POTUS and the children of members of the Armed Forces who happen to be born where ever their parents happen to be stationed overseas by their own government CANNOT? You are quoting a State Department manual to support this position? There is no third class of citizen "born a citizen but not natural born". No such distinction is made in the Constitution or in actual law. The applicable and pertinent law has already been posted. The US State Department Foreign Affairs Manual is not law.