Don' have a newer model but I would assume the fan should run when ever the frig is on gas or electric.
As for the noise I have put a muffin fan from Radio Shack in mine and I can tell its on only in the dead of night when all else is quite.
If you go solar attach the solar to the battery. The solar will work to charge the battery all the time and the battery will supply a correct voltage to the freg. As long as you design the solar greater than the freg, fan and controls, draw you will be fine.
Plus while in storage the solar will keep the battery topped off.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles