Not necessarily. The text of the 14th Amendment states:
AMENDMENT XIV
Passed by Congress June 13, 1866. Ratified July 9, 1868.
Note: Article I, section 2, of the Constitution was modified by section 2 of the 14th amendment.
Section 1.
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
Now, that second clause, "and subject to the jurisdiction thereof" is interesting. First, because it says "and" rather than "or", it is a qualifier on the first part of the sentence. Thus, you have to be born or naturalized and, in addition, be subject to the jurisdiction of the United States. To me, that implies that persons not subject to the jurisdiction of the United States are not citizens. Now, who is born in the United States but not subject to their jurisdiction? Illegal immigrants. It would be easier to amend the Alien and Naturalization Act, which is the law that defines citizenship, to exclude children of illegals, than to pass an amendment. In addition, Article I, Section 8 grants congress the power "To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;"
Thus, congress could, under its powers under Article I, Section 8, draft a law stating that those persons born to parents who are not subject to the jurisdiction of the United States by virtue of unlawful entry and evasion of that jurisdiction are not citizens.