I would. But he'd never ask or want to be. My dad even attended my baby shower and played games and everything. And was the only man there. I'd be honored if he was one of the people in the delivery room and was one of the first people to meet my child.
Not while giving birth but my dad did go in to pre-op with me when I was having my section with my DD. I was really nervous and stressed out and so was DH so my dad offered to come in with us to help keep us calm. He cut jokes with DH to help him keep his mind off things and he kept picking on me and bashing my evil nurse when needed to help me, lol.