Not really- the way any military unit is structured, you have to be present & accounted for, or your absence excused through channels. If President Bush had, in fact, not reported or walked away without proper protocols, the Air Police would have hunted him down & returned him.
There would have been no honorable discharge, either.
The "murkiness" you note- sloppy paperwork- is not uncommon, especially so many years having elapsed.
Yeah, that really doesn't surprise me at all. LOL
Thanks.