Off hand I'd say that Brian would be right on about a tarp trapping moisture, however my Alaskan has the front and rear "racks" which hold up the tarp I have and allow wind to circulate under the tarp. You have an AC unit and if you had those racks also I would not think that condensation would form as long as the tarp wasn't tied down too tighly. As long as you can see the breeze lifting the sides of the tarp and the top, then I would not be too afraid of condensation.
The point is; if you have sealed up the vents and the front/rear and window trim recently, you should have no problem with water intrusion anyway. My '76 isn't bothered by a little chaffing of the tarp to the paint as the paint is still in good condition. If you had a NEW Alaskan, I would not suggest the tarp and would hope that it had no leaking seams anyway.
Your option of putting it on a rolling frame to keep inside is the best possible option if you have room in your garage though...then you just need to insure mice don't find it as nice a place to use in the winter as you do in the summer!