I do this all the time and find it a low-stress way to start my vacation. And, in fact, I will be doing this at the end of October for a sailing on the Fantasy! I generally plan to arrive at MCO in the early evening the day before the cruise starts. The Hyatt was remodeled a few years ago, and the rooms are quite nice.
The details have changed a bit over time, but it's super-easy the morning-of. You should have plenty of time for a leisurely breakfast if you choose. The drive from the airport to the port is about 45 minutes, and buses seem to have started leaving by 9am or 10am in The Before Times. At least in the past, you didn't select a particular departure time from MCO - you just showed up down on the same level where the Magical Express is located. The boarding area for the
DCL buses is separate, however.
As you would expect, signage is good, and everything is well-organized. Check-in for the bus plus wait time can be anywhere from 10 to 30 minutes depending on the flow of passengers and timing of departures. So I usually just worked backward from my port arrival time to figure out when to head down.
You'll be able to check your luggage right there in the bus loading area and won't have to touch it again until it shows up at your stateroom. They transport it in dedicated trucks, leaving the under-bus storage for things like strollers and carry-ons bags. Be prepared to show your passport/ID/birth certificate and whatever you received (via post or email) for bus check-in. The exact paperwork for the bus has changed almost every trip, getting to be fewer and fewer pieces of paper.
The Hyatt used to have an arrangement with DCL where the hotel would actually collect your luggage from your room and take it down to the truck. But that service seemed to have been eliminated or highly restricted (they were a little vague when I checked in at the hotel) the last time I sailed in February 2020.
All of this is with the caveat, of course, that DCL could change their rules around departure times depending on how strict they are in a few months with port arrival windows. I've heard that other cruise lines are being very strict with people not being allowed into the cruise terminals until their arrival window. But that's now - who knows where we'll be in a few months.
Bottom line: I highly recommend staying at the airport Hyatt the night before your cruise. It's a nice hotel, and the logistics make for an easy start to embarkation.