Most definitely NOT.
As we can see, INTERNATIONAL LAW plays a role in births to aliens in the U.S. THIS arbitration ruling from 1876 (AFTER ratification of the 14th Amendment) CONFIRMS what Trumbull, Howard, and the U.S. Secretaries of State have ALL said about the 14th Amendment's requirements: children born in the U.S. to aliens are NOT subject to the complete jurisdiction of the U.S., are SUBJECT to a foreign power, OWE ALLEGIANCE to a foreign power, and therefore AREN'T U.S. citizens at birth:
"The umpire is of the opinion that it is not proved that the claimant was a citizen of the United States. The ground that he is so, is his own statement that he was born at New York, together with a certificate of baptism of a child who was born at New York, Beniguo being one of the names which were given to him; but it is not proved that the child then born and baptised was one and the same person with the claimant. Nor would the mere fact of his having been born at New York be sufficient evidence of citizenship. It is clear that his parents were both aliens at the time of his birth, and it is not shown that they were naturalized or that they or the child remained in the United States. The inference is to the contrary, and the umpire believes that the child in question, even if that child was really the claimant, though born in the United States, was subject to a foreign power and cannot without further proof be considered to be a citizen of the United States"Source:
I suggest you review further up the thread and examine the evidence already provided.