I wouldn't be so sure. I don't have any doubt CPS is going to try to re-unify this child (if not with the mother herself-although it's quite possible they will even try to re-unify child with the mother) then with her relatives.
But now there will be the advantage of her not hiding the baby, there will be mandatory parenting classes, and hopefully a web of support.
Now that this is completely out, she will have a hard time with the infamy, and may give her child the gift of anonymity through adoption.
No matter the out come, baby with new family, relatives, or mother, I am confident that there will be a network of security for her.