When I got injured at BMQ (keep in mind this was 4 years ago and things *could* have changed), I was sent to the AWT platoon once it was decided that my recovery would be too lengthy to stay on my regular platoon.
The staff at AWT told me that if I could heal within 3 months (90 days) I would return to platoon life within a week of where I got off (i got injured week 2). But if it took longer than 90 days, as would be the case with a fracture for example, then I would go back to week 0 no matter where I was when I got off. So while it sucks for the guy that is in week 11 and breaks his leg to have to go back to week 0, the thinking was that too much time had passed since he got off platoon, and a re-indoctrination of sorts would be good.
People learn a lot of bad habits on AWT, so re-indoctrination is usually a good thing. Plus it gives you a chance to bond with your new platoon. Harder to gain trust when you join in the last 2 weeks of BMQ.
As for exemptions, some (computer) written tests are exempted. Weapons test you usually run through again, CBRN also. And the EOs of POs (I don't remember which is which, whichever the more important of the two).