General Reply
Well long, long ago in another life, there happened to be a pilot able carrier, I believe it was CVN-74. It had operational elevators and would go anywhere there was water.
You had to fly it like a normal aircraft and could not do it at the same time as and aircraft, so it could only be for a multi player situation unless you just wanted to pilot a boat around.
It was also used in several AP as static objects as well as traveling a set course in a couple of air ports.
They are all capable of landing aircraft on board. The issue with a moving carrier is as was stated you can land but the carrier will continue to move out from under you.\
That is due to the ever changing location lat lon information. the aircraft doesn't recognize the carriers location as a moving point and DOESN'T UPDATE ITS POSITION.
I will gladly provide more information and steer you in the right direction. PM or email as you desire and I will respond.
There are airports with the carrier of which I have spoken. Do a search for CVN-74 or just CVN. I think you will be surprised..............