Only if it fits through the little scanner. If you took a soft duffle, it would fit because length doesn't matter. But remember, if your room isn't ready when you board, you will be schlepping it all around the ship with you.
Voyager of the Seas 5/03
Celebrity Solstice 2/09
Oasis of the Seas 10/16/10
Usually the cabins aren't ready until around 1:00, so you have to already carry your carry-on with you until then. Just turn over the regular luggage to the porters when you arrive at the pier, tip them a few dollars and it will show up in your cabin in a few hours.