He would most probably get access, don't worry it would never be full custody or anything, but he certainly would get supervised access simply because he has not seen the LO so they would do supervised access to help build a bond between them. Regardless of being forced to pay or not, he is paying, so in future, they will see he is paying and that will go in his favour.
The child’s father does however have to pay Child Support on demand, but is entitled to apply for a Parental Responsibility Order if the mother of the child is unwilling to agree to a Parental Responsibility Agreement.
If he is not wanting access, I would not worry too much.