I often hear how it is "Cheaper to use the Generator and the roof A/C"
I also do not believe it, But that is more feeling than anything I can prove.. But consider this.
When you engage the engine driven air compressor, it does suck a bit more fuel out of the tank, but 100% of teh horse power that it uses is used to compress gas .
When you run the gnerator only PART of the enegery the engine generates becomes electricity, I forget the precise percentage, but Thomas Edison optimized the design back when and not much improvement has been made since.
This power runs through wires (Loss) to a motor which like the generator is less than 100$ and that compresses the gas.
Losses every inch of the way up to this point.
NOW: the losses continue, but are the same in both systems so they balance out.
The dash AC cools the area just behind the DASH (Front seat area)
The ROOF A/C cools the house.
It gets hot enough, I run both.
Home is where I park it!