As long as the paperwork is filed properly, which isn’t always easy. It might be different now, but in the early 70s there were specific requirements about the number years the parent lived in the US versus abroad (so many years before the age of 14, so may years after the age of 14), and a letter from a lawyer basically confirming that they know the information to be true.
I don’t know how easy it would be to pass along that citizenship later, but it was not that easy for my mom to pass it to me before I was born. In fact, it almost wasn’t possible. If she had been one year younger, she would not have met the requirements for years lived inside the US.
