We've used Expedia to book WDW resorts before, and yes they do include ME. They will give you an address link to sign up for ME, and at some point they will send your WDW reservation number so you can do online checkin.
For our last stay last February, WDW did not have discount rooms available at our resort of choice, but Expedia still had some available. Using Expedia or Lastminutetravel.com or any other viable booking site to book WDW resort rooms should not deter anyone from using them, expecially if you can get a deal.