I can't say for certain but I can share my experience with you. I'm a birth doula and recently had clients that were in Taiwan for the birth of their second child. They were not married and their first child was born in Bangkok. The father was listed on that birth certificate. After the birth in Taiwan, they presented a document of verification, from the French Embassy, that he was indeed the father. After a lot of calling around it was decided that there was no way he could be listed on the birth certificate as the had no proof of marriage.
You two obviously have a marriage certificate so maybe it'll be different for you.