Yes, you can. Anyone can use DME for their arrival into MCO. It makes no difference what airline you are flying in on. Just put those yellow luggage tags on your checked luggage, then when you get to MCO, head to the DME welcome desk on Side A of the terminal, on the bottom level.
It's your return that could vary. Again, anyone leaving a WDW resort (with the exception of SoG, Swan and Dolphin) can ride the DME bus back to the airport. The different part is this...if you are flying out on one of the 'participating' airlines, you will be able to check your luggage at your resort, at a special desk area. You will get your boarding passes, and then you don't have to checkin at MCO....no baggage to check, you just head right for security. If you are not flying out on one of those 'participating' airlines, you will be told what time your bus will be leaving. You just take your bags with you, get to the bus, the drivr will stow your luggage underneath the bus, you will get to MCO, check your luggage, check-in yourself, and then head to security. That's the difference.