Touge/Whitelable/Checkboard
I think you may all be taking the FCOM diagrams too literally! They are designed to give a basic understanding of system distribution, rather than a full system logic explanation. There are in fact a lot of contractors/relays omitted, just to keep the diagrams simple.
If you attempt to start the APU with the battery's switched off but with ground power ON, the start will initiate but the ECU will sense a lack of fire protection. An AUTOSHUTDOWN will occur.
If you turn off the battery's with the APU running, ECU will sense lack of fire protection. APU will shut down.
Simple..... NO BATTERYS NO APU!
The explanation is in the AMM not the FCOM.