We seem to have this discussion every few years as well. First of all, you should check whatever the AF equivalent of the Officer Record Brief to determine what awards you are authorized to wear. If they're not on your ORB, you can't have them on your uniform. Technically, ADT for training purposes only does not qualify one for the NDM, I cited the regulation in a previous thread, but I haven't found the AF specific criteria (it should be the same). It seems like requirement has been ignored at Officer Basic for at least the AF and Navy, if not all three branches.
The GWOTSM requires 30 days service for a unit support the global war on terrorism. Once again, technically, you wouldn't qualify until you were in a non-training capacity. When I in-processed before internship, the personnel people "awarded" me both of these awards. I felt so honored.
In the big picture, it really just doesn't matter. I did however enjoy busting the chops of Army HPSP students going to interview with their NDM ribbon on their greens. OK, I didn't really do it, but in my head it was fun.
Ed