Lawyers are scum to begin with and Doctors aren't much better.
Cops and firefighters too......
If he were to pursue this, the courts would want to first establish paternity. To do this, they will ask to see the birth certificate and/or VAP forms (Voluntary Acknolwedgment of Paternity). If someone else is listed or no one is listed, then they will assume they need further proof by asking for DNA testing. Once paternity has been established, the state will start ordering child support payments.
The important thing to remember here is that establishing paternity does not guarantee a father any sort of rights over the child. It only established who the father is so he can help with the finances of the child through payment of child support. For him to gain any sort of legal rights, he would have to pursue that in court as a separate matter.
The issue of his record would more than likely come into play as the court evaluates what "the best interest of the child" is. This is a clause most states have and each state defines what goes into the assessment differently. You should speak with a licensed attorney in your state about the specifics of how your state would handle this situation. What I have given you above is just a general outline.