What if they chose a non-citizen to carry the baby?
It would depend on the state. In California, there was a case Anna Johnson v. Mark and Crispina Calvert (SO 23721) where the court concluded that if the genetic and birth mother are not one and the same person, then "she who intended to procreate the child—that is, she who intended to bring about the birth of a child that she intended to raise as her own—is the natural mother under California law.