yes - saving faith, just as John the Baptist had in the womb.
I have read where John was filled with the Holy Ghost. If faith was there, we have to add that ourselves, we have no scripture for it, that I know of. BTW, was John the Baptist ever lost???
Luke 1
41When Elizabeth heard Mary's greeting, the baby leaped in her womb, and Elizabeth was filled with the Holy Spirit. 42In a loud voice she exclaimed: "Blessed are you among women, and blessed is the child you will bear! 43But why am I so favored, that the mother of my Lord should come to me? 44As soon as the sound of your greeting reached my ears, the baby in my womb leaped for joy. 45Blessed is she who has believed that what the Lord has said to her will be accomplished!"
are you holding the sins of the fathers against the children?
I am sorry, but it is you that say, I was concieved in sin, and lay that charge to the infant. unless I misunderstood you.
besides, most reformed theologians hold to
at least the children of the elect are elect and many more hold to the election of all infants, dying in infancy - even Calvin:
from
Boettner's The Reformed Doctrine of Predestination
Ch. 11 - Infant salvation