Single father about to join army. Do I get BAH for my son?

I'm Considered a single dad because my me and my fianc� aren't married yet. We are together and we both care for our son equally. The recruiter wants us both to write a letter saying that I'm not financially responsible for my son and that he lives with his mother. If I do this will I get financial benefits for my son while I'm in basic training. When I say financial benefits I mean health insurance, BAH and separate rations. If I write this letter will I forfeit these benefits?