Short answer NO (I mean you could do it but the job would cost more than is practical) The reaons is this, Detecting the presence/absence of 120vac is very easy, But detecting when you run out of Propane.. Not so much.
The mother board on the fridge DOES have a flame sensor, if it tries (Likely 3 times) to light the burner and fails to do so it will set off the Fault detector.
But there is no provision to cause that to switch to A/C and while that light is lit the fridge is locked out
Easier would be to sense that light and generate an audio alarm so you manually switch it. Or refill a bit more often.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times