Yes they will.
To speed up the required advance reservation for Magical Express, have in mind a flight number, any flight, any airline arriving in Orlando at the time you are ready to go to Disney.
The reservationist may or may not ask for this information.
You must not use the yellow tags at first and you must claim your checked bags and bring them to the hotel. The Orlando Airport Hyatt does have a special procedure where you check out and put the yellow tags on the bags and the bellhop (for a tip) takes them down to Magical Express to be delivered to your room. Or you can take the bags to the bus yourself.
