If there is space available on the cruise, they can get you on. Call the cruise line and ask them. They can email you your information or even over night the paper documents to you if need be.
Your only issues may be getting airfare if needed but even that is still outside the typical 14 day advanced booking timeframe.
Go for it.
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