Absolutely no way possible would I do that!!! Especially if its paid for. There's a good reason the dealer is offering a straight up trade plus a little extra for your truck! He stands to make money on it where I bet he could hardly give away the dually gasser. Not there is anything wrong with it, its just not nearly the truck you already have that's paid for!
As far as sitting goes, I see no problems with it so long as it's fired up occasionally and battery and all fluids topped off. What's the difference in a gas truck sitting vs a diesel with all things equal?