I haven't flown SW before. We leave for Disney in five days! I just purchased the EB for our flight home. Does this mean I don't need to worry about checking in or printing boarding passes until Magical Express drops us at MCO?
Correct. No need to check in. It will be done automatically 36 hours before your flight time. You can go on the SWA site 24 hours before the flight to check on your numbers.
If you use Resort Airline Check-in to check your bags, you can get your BPs then. You also can just have the BPs printed at the airport by a skycap, at a kiosk or even at the ticket counter.