This is certainly a concern as the father does have parental rights unless taken away by the court. Thus, the threat is real.
However, if the father presses the issue, your wife should consider filing for back child support from the date of the child's birth to date. The sheer possibility that he may be hit with all of these fees at once is enough to make most people back off - child support over 15 years would be in the tens of thousands of dollars.
Also, if the father were to seek custody, he would have to prove that it is in the child's best interest. In determining this, the court looks at the relationship with the child, child's preference, stability of the home, home environment, character of parents, school issues, etc.
In this case, the father has been absent for most of the child's life, which is going to be a great concern for the court. Even if they're around each other now and have a decent relationship, it's not going to make up for the past decade or more of his absence.
In general, I don't think a court would modify custody and grant his request if he made one. However, you never know what a judge may do.
I think the best defense if he tries this is to file for back child support and make him face the possibility of having to pay your wife for the last 15 years of care for the child.