Here's what happened to us:
We did not receive luggage tags for our 5/16/05 trip. When we arrived, we went to the ME desk, and they had our names in the computer for transportation to SSR, so no problem getting onto the bus. I gave them our luggage tag numbers from the airline and and a description of our luggage and they said "No problem. Someone from Disney would pick up the luggage from the baggage claim and transport it to our hotel." Now, when I made my flight ressies, I gave Delta airlines my cell phone number. We had arrived at SSR and been in our room for all of 10-15 minutes when my cell phone rang. It was someone from Delta airlines calling because our luggage had not been picked up off the baggage carosel. The man asked if we were staying on Disney property and using ME. I said yes, and he said he would take the luggage to Disney for us. This was sometime between 5:00 and 5:30. We left to go to the HDDR around 8:00 and the luggage still had not been delivered. When we arrived back at our room after 11:00 it was there, so I don't know exactly what time it arrived.
This said, if I had to do it again with no luggage tags, I would pick up the luggage myself and take it to the ME desk. Who know what would have happened to my luggage if Delta hadn't found my cell phone number in my reservation?