DME and airline checkin are separate.
As long as you're flying on one of Disney's partner airlines, you can get boarding passes and check your luggage right at the resort. Doesn't matter if you our using DME or not. Partner arlines currently include: AirTran Airways, Alaska Airline, American, Delta, Continental, Jet Blue, Northwest and United/Ted
AirTran was just recently added so I used this service last month. It was fabulous. Checked our luggage, got our boarding passes and had bell services hold our carry ons all in one stop. We happened to also be using DME this trip and our resort pick up wasn't until 3:00 at Pop Century. So we headed to the GF for breakfast and the to MK for one last ride on the train. It was sooo nice not to have to lug our bags through MCO. Just a quick wait for security and Voila!
However, if you are flying domestically on one of the non-partner airlines, you can check in online if you brought your laptop with you. Any concierge desk will be happy to print out the boarding passes but the wait can be quite long at certain times of the day.
You could also opt to use a computer at one of the many business centers on property to check in and print your boarding passes.