Assuming the starting SOC of the traction battery is high and the car is outside with heat/AC off. Manual seems to have no prohibitions on it, other than the exhaust fume thing. I'm assuming the engine would start at SOC of 33% or so. The traction battery would make a very large dashcam battery. edit: Have to use the metal key and possibly turn off the auto power off feature to lock door and keep energized. Also, the gauge cluster is lit up, drawing attention. The three-press trick on the door lock button on remote turns on the hvac system to auto, and probably only runs for a certain amount of time to warm/cool the car.
I don't know about any gen 5 details that might be different, but yes, through gen 3 you certainly can, if you use the metal key to lock. And yes, the dash lights will attract attention, and the engine will start and stop, attracting attention, and anybody who breaks into the car will be able to drive away. Once they turn the car off they won't be using your key to start it again, but they could be 500 miles away by then.