The cruise lines won't "guarantee" anything about a flight you do not book through them - and the ride from the ship in Citivecchia (sp?) to Rome airport is a long way - and could be up to two or three hours if traffic goes against you. The port is about 70 miles away, and you will be amidst morning traffic going into Rome.
I wouldn't be surprised if the Celebrity 10:00 am flight offering leaves the ship at 6:00 am. You won't get off the ship that early without special permission - which they "might" give you but you would have to arrange it in advance. As for the 11:30 flight. You would have to be off the ship by 8:00 am, I would recommend. That is probably do-able.
Personally, I would check to see if the cruise line offers transportation to the airport even if (you decide) you are not booking your flight through them. That way you will at least get off the ship in time.
The above is just my opinion and I reserve the right to be wrong. ;-)