I can't answer the question of if the Captain would allow it, but I can say that your reception won't be the best in your cabin. The ship will act like a big Farady cage unless you have a balcony cabin and want to use the radio on the balcony.
You would have to call the cruise line and ask if there are any rules about this. Its not something that comes up much other than people wishing to use walkie talkies on the ships (which are allowed) But the higher power of your xmitter is something different.
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, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013