Jessica- Have you checked out the discussions on the Civ to Rome train in the Europe port chat? If not you should at least read it.
As far as the timing goes, it might be much less stressful to just wait and purchase your tickets at the station. Print out a copy of the schedule so you know what times you need to be at the station and play it by ear.
You can certainly make the train you have scheduled IF all goes well and you get off the ship in the first group (and customs clearance happens quickly but that could take time). But the port won't let you walk through the port area, they shuttle bus you to the port entrance and the train station is a couple of blocks from there. If you end up waiting for the shuttle to fill up and depart from the ship, that make take time too.
All said and done, its not worth the risk to prepurchase the tickets. You can also buy a combination ticket that provides the train (round trip) AND an all day Rome subway pass. That may work better for you.
The uncertainty of what time you will actually be able to get off the ship is concerning. I wouldn't risk it UNLESS the ticket can be used for any Civ to Rome train that day.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013