Also unless the court ( judge oks it and rules on it) it is merely a contract, and if the judge rules it not legal, it will not be binding.
Often , esp if the custodial parent gets welfare the state will go after the other parent to be paid back for money spent on the child, I doubt that an agreement not ruled on as a court order would be binding on this.
Most states ( not all) will not normally ( note but sometimes) allow one parent to sign away obligation to child support. Unless there is someone willing to adopt the child ( new step parent)
You can sign over any rights to visit, to custody, but the state holds and requires some obligation ( not right) to pay support