Hi Dloebrich,
Congratulations on the new Cyclone. Let me divide the answer.
If you have Norcold or Dometic RV gas absorption refrigerator, it runs off either 110V or propane, so you can run it while towing whether or not the generator is running. Many people do so, although some leave it off while towing for safety reasons. If you do run it on propane, keep in mind that while running on propane there's open flame just inside the side wall of the trailer. If you pull up to a gas pump, there's some exposure to igniting gas vapor. Diesel is not as explosive as gasoline, but the guy on the other side of the island could be pumping gasoline. So it's smart to shut off the frig when refueling.
If you have the new Residential Refrigerator Option, it will run on battery while towing, so you don't need the generator for that.
To run the A/C, you would have to run the generator. I've done that with our Propane generator on a 98 degree day but didn't find it very effective. When we got to the campground, it was still hot and took a long time to cool the trailer down. Others have found it helpful.