Long story short....every single person arriving by plane, into MCO, can check their bags and have them handled by DME as long as they have attached the yellow DME luggage tags on them. It does NOT matter what the airline is. Period.
'Participating airline' matters only for your return flight, from MCO to your home airport. And it matters only for checking your bags at your resort and getting your boarding passes issued then, vs checking bags and getting boarding passes issued at MCO. If you are not flying on a 'participating airline' for your return flight, and Virgin America does not participate at this point, you just take your bags with you to the DME bus. The bags will be loaded underneath your bus, and then handed to you when you get to MCO. You will then check your bags and get your boarding passes the 'old-fashioned' way...at the airline counter.
But you still get to ride the bus, you still get your lugggage delivered to your resort room upon arrival at WDW.
When Disney says 'participating' they are talking about the RAC system, not DME. RAC (remote airline checkin) is not run by DME or Disney. It is an entirely different operating system. Think curbside checkin...but the curb is a loooooong way from MCO.