The answer is YES but you ought to talk to Royal Caribbean because it is almost a certainty that you will have to make them aware that you intend to bring it. .. Neil.
As Neil & Ida state, it is IMPERATIVE that you inform RCI of the scooter's dimensions before you travel, since a lot of scooters simply won't fit through the stateroom doors unless you have booked a disabled accessible stateroom.
We recently took two elderly ladies on Independence, one in a wheelchair and one in a motorised scooter thingie. We had booked a disabled access stateroom for them and everything was fine there. However, it was impossible to get the motorised scooter into our stateroom when the ladies came to visit purely because of the size of the thing.
Once you sort out stateroom access, you will have absolutely no problem anywhere else on the ship.
But remember - TELL RCI BEFORE YOU BOARD!
We saw a number of people with these scooters last week on the Independence and taking them ashore, there were a number of RC trips for people with mobility difficulties but you still need to be able to climb up onto the coach and the ramp on and off can be very steep at times although all the shore staff rush to help any passenger in difficulties.