If he doesnt want to akcnowledge the child, then no one can force him to do so. If he doesnt sign, then it means he doesnt want to acknowledge the child as his own, so why bother send financial support?
Once he signs, he is legally obliged to provide financial support to the child and ofc acknowledges that he is the father of the child. Ang alam ko, hinahanap ang MC ng magasawa bago pumirma ang magulang sa BC ng bata unless it is not being practiced by the hospital or so anymore.
However if he doesnt sign the BC, the issue is when the mother files a complain in court, she might get a chance to request the court for father-child DNA tests, where the father and son must comply afaik.
Acknowledging the child has nothing to do with the mother's intention imho.
Kung handa kayo sa katotohanan, at para makasiguro kayo ng bf mo, bakit hindi nyo subukan ang DNA tests bago pa man mag complain ang babae? The test would give you some kind of peace of mind at a cost of 20K more or less.
Kaya lang, discretion is a must upon doing it at maaring hindi pumayag ang nanay ng bata. Catch 22.