They couldn’t change the status of any existing “anchor persons” but could future ones.
I don’t see why not; if one or both parents are illegal aliens that, in my mind, makes the baby or babies all illegal aliens and subject to immediate deportation.
The Amendment was originally interpreted by the SC to insure that the children of slaves (not brought here voluntarily) were granted citizenship and subject to all the laws and rights of any ordinary white citizen.
It was not intended to provide a welfare scam to illegal aliens in the 20th and 21st centuries.