If Archie had been born in the USA, would he be a NBC, since his mother is a NBC?
No. The rules of 1787 were that only men could pass on citizenship. The only way a woman could pass on citizenship in 1787 was to be unmarried. If a woman was married, the child acquired the citizenship of his father, and so did the woman, regardless of what her previous citizenship was.
Women were not able to pass on citizenship until the cable act of 1922, and it is nonsensical to think that an act in 1922 could undo the meaning of a law from 1787.