The system to have DME automatically deliver your bags without DME tags has been a standard procedure since Day One. In know, because I used DME on Day Four, and back then there were HUGE problems with getting DME tags out in time.
The explained the procedure that exists to this day. You skip baggage claim, and check in at the DME Welcome Center like normal. Part of the CM's "script" is to ask if you've DME-tagged your checked bags. When you say "No," they'll ask for your baggage claim ticket numbers, as well as a physical description of the bags (as matched to a photo array).
I received my tags about 14 hours before I left for my trip, so I was prepared to do without. A DME CM at the time suggested we tie some very identifiable ribbon to each piece of checked luggage, and then bring a swatch of that ribbon to the DME Welcome Center with us, to better aid in matching the bags.
Like goofy4tink said, we haven't read about any wholesale problems of people using this Plan B.