''....Current orthodontic appliances for continued treatment (V53.4) are disqualifying. Retainer appliances are permissible, provided all active orthodontic treatment has been satisfactorily completed. Individuals undergoing orthodontic care are acceptable for enlistment in the Delayed Entry Program only if a civilian or military orthodontist provides documentation that active orthodontic treatment will be completed prior to being sworn into active duty....''
Derived from Department of Defense (DOD) Directive 6130.3, "Physical Standards for Appointment, Enlistment, and Induction," and DOD Instruction 6130.4, "Criteria and Procedure Requirements for Physical Standards for Appointment, Enlistment, or Induction in the Armed Forces."
Personally, if your teeth are straight now and you no longer 'need' it, I would leave it at home until you return. I wouldn't have wanted to bother with it at BCT, or risk losing or breaking it.