If he can be added on at a later date then I think, well if i were you, i would say fuck him and do it without him, do what you want safe in the knowledge that if he does miraculously become a decnt father you can put him on if you want to.
If he cant be added on (although from looking at that link and reading the application form im pretty sure he can be) i would still be tempted to say fuck him and leave him off but I think i would find that a more difficult decision to make but really its just a bit of paper, noone takes much notice of a birth cert apart from people filling out forms who dont care whats on it. The rights you'd be giving him by putting him on are much more significant.
But thats just what id do, as CD said you have to do whats right for you and Joe and noone else.
Im just trying to keep my mind off useless half arsed contractions that couldnt push a fart out, nevermind a baby!!