I doubt it.
We live in a country where being feminine is generally considered terrible, and I don’t see anyone who wants to join our most masculine of institutions doing that on a whim and on public medical record.
Having said that… perhaps we should just avoid letting liars into the military?
It’s interesting, but it seems like every time a conservative voices a concern about transgendered people, the actual concern is that a cisgendered person will be deceitful or otherwise commit some evil.
So why not deal with that instead of people doing no wrong?