It is possible
For those that are interested or in a similar situation: AFMAN 36-203, AFRC Sup I, para. 1.11.1.3 states that with prior approval of HQ AFRC/ A1CSA, we can appoint someone to the civilian (Part A) side of the ART job while waiting for appointment to the military (Part B) side.
Therefore, it is possible to be an ART while on terminal leave with active duty. You just have to sign a memo stating you will be seperated from the civilian position if you cannot fulfill the military requirments (that begin after your date of seperation).