Not necessarily.
If the NCP has a criminal background, the state can pursue unilateral termination of that parent's rights without a pending adoption. An acquaintance of mine (not in GA) is going through this procedure right now, in conjunction with a child whose mother is already incarcerated, and father enters and exits jail like a revolving door. The father's parental rights were terminated by a judge pursuant to state action while the child was under foster care. The foster parents are now pursuing adoption.
Another thing to consider is that, while I am *not* asserting this is the case in the OP's situation, if the state believes the CP is maliciously excluding the NCP from the child, hence not pursuing child support et al, the state may exercise discretion to have an attorney ad litem appointed to represent the child's interests. Child support is for the benefit of the child, not the CP.