Trying to get the girl here to have the baby when he is not even sure it is his, nor does he want to marry yet would basically be screwing the immigration system.
It is irrelevant if she has the baby in the Phil, and would probably get better care there. If it is his, then getting British citizenship in the future is not a problem.
As for if it's not his, and putting his name on the birth certificate, don't even go there.The birth certificate is for the real parents, not adoption.