Darla,
For DoDMERB to issue a disqualification for braces they must have had a report from your son's orthodontist saying that the braces would be off after induction day (DoDMERB uses a rough date of 1JUL). Waivers for braces at the academies are very rarely given.
Your son's admissions package will continue to be processed regardless of your son's medical status, so that shouldn't be a worry.
There are a couple of options that you have. One is to speak with your son's orthodontist to see if his braces can be removed prior to induction day and submit a letter stating so to DoDMERB. If your orthodontist is unwilling to do that, you can pursue a waiver, again, those are rarely given for the service academies. ROTC will grant waivers for braces as long as they will be removed prior to graduation. Or wait until the following year to apply to the academy (provided the braces will be off).
There are multiple reasons the academies are so strict on braces. At all the service academies there are limited orthodontic services, othodontics are very time consuming and during the 4th class year there is very little time for appointments, and the 4th clas year is very physically demanding, and the chance that there could be damage done to the braces or lips due to the braces is pretty high.
If you have the orthodontics removed early be aware that there is a chance that the teeth can revert back to their previous position. A permanent retainer (or even a removable retainer) can be used and it is not a disqualification.
If the letter that has been sent in by the orthodontist states that the braces will be off before induction day, I would give DoDMERB a call and point that out. The disqualification can be removed very easily.
I hope this helps, and let me know if you have any other questions!