Yes, you can. Just do not put on the yellow luggage tags you get in your info packet from DME. The only issue I have with grabbing your own luggage is this...if you flight uses Side B of MCO, then you have to go to baggage claim on Side B, get your luggage, then go back upstairs to the main level and then go across to Side A, then back down to the bottom level to use DME. This isn't an issue if your flight uses Side A.
But, you can grab your own bags, then go to the DME check-in desk. Your bags will be put underneath the same bus you are riding on. And to those of you that do get your own bags...something to keep in mind. Any time someone touches your bags..bus driver, bell person..whatever...they should be tipped. If you use DME but don't have any luggage, then no tip is expected. Just a tidbit of info.