Yes, your cell phone's other functions will still work.. but (there is always a but)
If you use a CDMA service (Verizon and Sprint) the phone gets its tiem via GPS when in its network. (Some people don't know this, but your cell phone's clock is dead on...) So, without the network, the clock on the cell phone can get WAY off depending on the accuracy of its circuit.
Also, if you do try to use it for the alarm clock and or camera, switch it to "stand alone" mode if it has one. This is where is does not try to talk to the cell network. If you are out of coverage, the battery life will plummet because the phone will go to "full power" trying to connect.
If all you want it for is the alarm, you may be better off just setting a wake up call on the cabin phone then messing with you phone.
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