Why not go to the courthouse and just see what your options are? I heard that here in Washington state if you want to adopt a baby, like say you meet someone else, get married and want him to adopt your baby making him the legal father you have to put an ad in the local newspaper(where he lives) and if the birth father doesn't respond you don't need to contact him in anyway and the adoption is approved by the state. Also, if your parents are the ones wanting baby they could look into their grandparent rights if your state offers that. That way if you are off in the navy and biological father decided he wamts baby they would have custody and be able to make all the legal decisions. I'm pretty sure..
I beleive if he isn't on any legal papers such as birth certificate or baby having his last name. Then he pretty much doesn't exist. So his permission is not needed for your parents to adopt your baby. It would be no different than a woman who has no idea who her baby's father is. He would have no say. But you can always check with the lawyer or who ever maybe handling your adoption case.
If he is not on any paperwork and child doesn't have his last name there is no connection you can do whatever you decide I would just say you don't know who the dad is if anyone asks