No.
Your baby would be a U.S. citizen because you are a citizen. You will have to register your baby’s birth with a consulate or embassy while overseas.
Three types of citizenship are recognized by our government: native born; naturalized; and citizen-by-statute (derived citizenship from parents). All have equal rights. All can serve in Congress, either as a Representative in the House, or as a Senator in the Senate.
The following link will take you to the government’s own Immigration Service web page describing the three types of citizenship.
Natural born Citizen is NOT a type of statutory citizenship.
Natural born is ONLY an eligibility requirement for the U.S. Presidency per Article II, Section 1, clause 5, of the U.S. Constitution, and requires, as per the Founders, the President to be born in the United States (jus solis) AND of two citizen parents (jus sanguinas).
The definition of natural born Citizen appears in the holding of SCOTUS’s unanimous decision of Minor v. Happersett (1874).
Minor v. Happersett, 88 U.S. 162 (1875), is a United States Supreme Court case in which the Court held that the Constitution did not grant women the right to vote...
The Minor v. Happersett ruling was based on an interpretation of the Privileges or Immunities Clause of the Fourteenth Amendment. The Supreme Court readily accepted that Minor was a citizen of the United States, but it held that the constitutionally protected privileges of citizenship did not include the right to vote.
SCOTUS rejected Minor’s argument that she was a citizen under the 14th Amendmnet of the U.S.Constitution, and examined her eligibility, concluding that she belonged to the class of citizens who, being born in the U.S. of citizen parents, was a natural born Citizen, and not covered by the 14th Amendment. This holding has been used in 25 consequent SCOTUS decisions since 1875.
No one has the RIGHT to be President.
The eligibility requirement of Natural Born Citizenship (jus solis + jus sanguinas: born in the U.S. of U.S. citizen parents) must be viewed as a means to prevent split allegiance for any President of the United States.