@EW73 + no sponsor
I've seen FR aircraft operating without an APU in accordance with the MEL; others using ground-source airconditioning when available; and many using the APU if the GPU is unreliable or when outside air temps are below 10 or in the twenties. The fuel burn is not an issue; it is normal practice in FR to use the APU in these circumstances. Waiting for a slot on battery power alone for more than a few minutes is contrary to policy and most unlikely for all the reasons you mention!
Let's wait for the facts.
