Baby flying with tourist passport.?

Okay, We are stationed in Germany (husband is Army) and I had a baby at the end of March. My little boy was born with a bilateral cleft lip & palate, and although were happy with his cleft team here (an hour away) we decided recently to apply for an early return so his doesn't have to switch teams mid-treatment. The issue is, we have an appointment july 7th to apply for his American birth certificate & no fee passport but they said it can take up to 32 weeks to get back (no fee passport),.. 32!!! & most likely at the very least 12-13 weeks. Can my son travel HOME on a tourist passport with orders as long as we have APPLIED for the no-fee? What I'm understanding is the military will pay for our tickets as long as we have applied for the no-fee, but we don't necessarily have to use it. Is this correct? Thank you. Oh- I should add that my husband intends to stay here in Germany and finish out here.. I don't know if that makes a difference. x