I did this in November:
Arrived at MCO right around 8
Arrived at POP Century around 9
Checked in, found room, dropped carry ons, went to the Food Court for a snack and refillable mug.
I stayed awake until about 11, and no bags. I had a well prepared carry on, so no actual need for my checked bag. I called Luggage Assistance, and asked them to hold my bag until the morning.
I got up the next morning, and there was a message on my room phone. It was a voicemail from Luggage Assistance, left at about 3am telling me they had my bag, and to call them to arrange delivery.
I jumped in the shower, got ready, and called them to say anytime would be fine. I then headed to the food court for breakfast, and by the time I got back to my room, the young lady from Luggage Assistance was closing the door to my room. Total time from my phone call to this was maybe 40 minutes.
So yes, they WILL hold your bags for you if you call and ask them to once you're settled in your room.