I'm doing exactly this for our cruise next March. We are arriving the day before and staying at an airport hotel. These are the instructions in our travel summary.
If you plan to be in Rome prior to embarkation day and wish to return to the airport for your transfer to the pier, please meet at the airport location below and locate a Princess Representative to confirm your transfer time to the pier. Location 1: Terminal 3, Arrival Area Meeting times: 8:00AM - 11:00AM In case of flight delays, please call the Princess Enroute: 1-800-545-0008 If you cannot locate a Princess Representative at the airport, please call locally at +39-06-42881472, +39-06-42881642 , +39-348-8105-245 Unused transfers are non-refundable