Behavior when car is off?

No, off is off.

 

It took me a while to figure this out - press start button with brake pedal = car is on. When car is off, press start button without brake pedal = accessory mode. Press it again to get ignition mode. Press it again and the car turns off. I'm still trying to figure out what I can do in accessory vs ignition vs on. There's probably something in the owner's manual that explains.
This doesn't really answer your question, but hopefully gets you started on all the different ways it can be "on." Good luck!

 

I think you'll find that the radio/entertainment will work in accessory mode (one push without the brake) and the air conditioner, power windows, everything else will work in ignition mode (two presses without the brake). But, these are running off the 12-volt battery only, so not much capacity. Better to put the system in Ready mode (one press with the brake) so the traction battery comes into the equation, and the ICE will run when needed to recharge the traction battery.

 

Battery "danger" comes on velvet shoes...

My 2 cents: never just hang out in the car. Use it to get you places, park it, shut it down, get out and about.

 

The AC compressor runs from the traction battery, not 12V. It should run only in READY mode. The ventilation fan does run from 12V, so you ought to be able to exteract any remaining coldness from the evaporator, but it shouldn't be making any more cold.