For inbound travel, the airline makes no difference.
For return travel, you can use Magical Express with any airline, but you can only use Resort Airline Check-in with specific airlines. Spirit is not one them. So, if you're flying Spirit, it's simply a matter of having your luggage carried in the luggage hold of the DME motorcoach, and checking your luggage with the airline (or with a skycap for the airline) once you get to the airport.
From this FAQ:
http://disneymeetings.disney.go.com/dwm/services/detail?name=DMEAttendeesFAQDetailPage
RESORT AIRLINE CHECK-IN and Out-Bound Luggage Handling
Q: What is Resort Airline Check-in?
A: This service offers remote check-in, allowing you to check your luggage and receive your airline boarding pass at the Resort. At this time, remote check-in service is only available for guests flying domestically on the following airlines: American, Continental, jetBlue, Delta (including Song), and United (including Ted). Additional airlines may be added at a later date.
Q: What do I do with my luggage if I'm not using the Resort Airline Check-In service?
A: Please take your luggage with you on the bus or other transportation you have arranged to return to the airport.
Q: Where are the Resort Airline Check-in Desks located?
A: The dedicated check-in desk will be located in or near the lobby or outside the Resort entrance.
Q: What are the hours of operation for the Resort Airline Check-in Desk?
A: 6:00 a.m. to 2:00 p.m.
Q: Do I need to ride the Disney's Magical Express motor coach to the airport in order to participate in the Resort Airline Check-in?
A: No. After utilizing the Resort Airline Check-in service, you can either take advantage of the complimentary motor coach transportation to the airport or arrange your own private transportation. Your checked luggage will be transported to the airport regardless of which transportation option you choose.