I at first read that to mean that applying was enough to consider the child a natural-born citizen.
What I believe is that the parents must complete the naturalization process before their child is born for the child to be a natural-born citizen.
I do agree that any citizen is eligible for state and local offices, as well as for Congress, given the residency and age requirements. Citizenship of parents is not a factor for Congress.
-PJ
“... parents must complete the naturalization process before their child is born for the child to be a natural-born citizen.”
Correct.