He really should contact his recruiter to get a definite answer to your question. I honestly do not know the answer to your question but one question that may be asked is: Are you married or will you be married by the time he heads off to basic? If you are married then there should be no need for a DNA test and you and the baby will be covered under his insurance which is Tricare.
Congrats on your baby girl! I hope she arrives uneventfully.