But no - according to most views of the law back in the 1700’s women were inferior to men according to natural law.
Our view of natural law has changed, and equality under the law means that men and women are to be treated equally under the law.
Thus U.S. law is to always reflect our best understanding of natural law - and it is NOT the natural condition of women to be unequal and subservient to men - despite the protestation of most 18th century men otherwise.
As to what the term “natural born citizen” meant at that time - under English law the children of foreigners born in English territory were “natural born” - so the meaning as known and understood by our founders would not be confined solely to the children of citizens.
Vatell’s reasoning would not grant citizenship at birth to the children of foreigners born on the soil. It is not that he would grant them citizenship of a lesser kind at birth. They would not be citizens at all.