Well, a lot depends on what state you're in. In many states, like min, Florida, if he's not on the birth certificate, and there has been no paternity established by the courts, he has no legal rights.
What he does have are 'putative father's rights.' Any man who believes he may have fathered a child has the right to petition the court for an action to establish paternity through DNA testing.
From what you have described, he probably won't do that, so if your daughter says no, it's no.
Whether or not that is good or bad for the child is what you have to ask yourself. I personally don't believe in the 'new age philosphies' of not badmouthing the other parent, 'and it's still their parent.'
We can't teach our children about responsibilities and consequences if we don't have consequences for parents who don't take care of their own children. It sends a mixed message to a child and it holds no one accountable.
That being said, I think the child should know the truth about his or her biological parents and know that they are a bad example of what a parent is and that that is why they are not permitted the joy of being with their children.