As far as I know, the application status is only for an appointment offer (or not). An LOA is considered a conditional offer of appointment, so that status would show (only if you are offered one...it will not tell you that you aren't receiving one).
What will also not show is whether you are scholastically, medically, or physically qualified. However, you know if you are medically qualified from DODMERB. Bottom line, is you are unlikely to see a change in the application review status until early next year unless you are offered an appointment/LOA early...or medically disqualified...might be some other exceptions, too. So for candidates...don't expect that the application status will show your scholastic/board status!