Pretty much. However, I forgot to add an important distinction: Congress could at will redefine the status of children born overseas. There is no constitutinoal provision there. However, the 14th Amendment is concrete.
Just because the Constitution is silent on a specific matter is NOT assent for Congress to act; indeed, quite the contrary. Congress only has the powers that the Constitution specifically enumerates. Congress does have the Constitutional power to naturalize the child, but as far as I know naturalization applies only upon the birthdate of majority.
Prospectively, anyway, not retrospectively.