Actually, no.
The foreign-born child is a citizen AT the moment of birth, not BY the act of that birth, at least not any more than it makes him/her a live human being, which is the requirement of any US citizen. My dog, born here, is not a citizen. Not enough chromosomes.
However that NBC status can be revoked if that NBC child fails to commit certain acts; residency, etc. or commits certain acts, renouncement, etc.
But citizenship by birth is established by the mere fact of birth under the circumstances defined in the constitution. Every person born in the United States, and subject to the jurisdiction thereof, becomes at once a citizen of the United States, and needs no naturalization. A person born out of the jurisdiction of the United States can only become a citizen by being naturalized, either by treaty, as in the case of the annexation of foreign territory, or by authority of congress, exercised either by declaring certain classes of persons to be citizens, as in the enactments conferring citizenship upon foreign-born children of citizens, or by enabling foreigners individually to become citizens by proceedings in the judicial tribunals, as in the ordinary provisions of the naturalization acts. - U.S. v. Wong Kim Ark, 169 U.S. 649, 702-703 (1898)
http://openjurist.org/169/us/649