We have done this a few times now, most recently last week between Pop Century and Contemporary. We called the night before letting them know we needed the move. This time they couldnt gurantee us a time because the luggage truck had flipped over that day, but under normal circumstances it should be there by 4:00-5:00.
We left our room with all the bags there at about 7:00 am. When we checked in at the Contemporary about 3:00, everything was right there for us (the room wasn't ready, but thats another story. )
We have also taken all our luggage ourselves in a cab when we wanted to check in early another time.