Do paedobaptists suggest that a baptised infant is really 'born again'?

This question is for Protestant Trinitarians and addresses the divide among the various denominations of Protestantism, particularly Presbyterianism, Congregationalism and Anglicanism, who baptise infants rather than adults. I was, myself, 'baptised' as an infant, but late in infancy as my father was a Church of Scotland clergyman in the remote Highlands of Scotland and was not permitted to baptise his own child, so the matter was delayed and I remember it vividly at the age of five. But after conversion at the age of sixteen I volunteered to be baptised in a Baptist assembly (and my father graciously attended). Among all the arguments to and fro about circumcision and 'sanctification' it is still not clear to me if those who baptise infants actually claim that the child is 'born again' in the various senses in which that term is used in the New Testament, that is to say : born from above (*anothen*); born anew (*anagennao*) ; born again (*paligenesis*) ; born of God ; and born of water and Spirit. What exactly do paedobaptists believe is happening (in New Testament terms) during the ritual of placing water on a baby? And if they regard it so (that this is genuine 'new birth') then can such infants not be recovered if they (initially) reject the gospel in childhood since that would be regarded (in New Testament terms) as being a castaway, having been 'born again' only to reject Christ?