Yes you are taken straight to the ship on a bus, you identify your luggage on the quayside, label it and it is delivered to your cabin in about 2hours.
Not strictly correct, I have just returned from this cruise, you are met by Thomsons reps at departure airport, your luggage is then tagged with your cabin number. You check it in as normal and when you land at La Romana you board a bus without having to go through any form of passport control or immigration, your luggage is delivered straight to your cabin. On the return, you leave your luggage outside your cabin on the night before, by 3 am if my memory serves me correct. Your luggage is delivered direct to the airport and you have to then identify it and check it in as usual. I think they do it this way because the transfer operators do not have coaches with the capability to store passengers luggage in a boot. Although the coaches do not look quite what we would expect, they do have air conditioning and it's less than half an hour transfer to the ship......enjoy your cruise .
My luggage was labelled at Gatwick and was outside my cabin door about half an hour after I boarded the ship.