We just did this on our cruise a few weeks ago. (We actually stayed at the Radisson's sister hotel, The Quality Suites Cocoa Beach, then drove down to the Radisson and left our car there and took their shuttle.)
Everything went very smoothly for us. We booked a time for the shuttle when we arrived at the hotel the night before. Then we dropped our bags off at the front of the hotel and DH went to park the car in the back. They loaded the bus fairly quickly and took us straight to the port.
We were dropped off at the terminal, tipped the porter to take our bags and went off and had a truly fabulous vacation.
When we came back, we went right to the spot where they dropped us off and they were there waiting for us. We went back to our cars, and were dropped off with no problems (after we tipped the driver of course.)
I have read of other people on these boards that have had problems with drop off and pick up times. I think the main thing is that as long as you are flexible with your timing it is a great way to go.
We were going to WDW after, but knew that we wouldn't be there for park opening. We were very relaxed and non-stressed after all we had just spent a awesome week in the Caribbean! Good luck and enjoy!!