Definitely shuts down the APU. Ask me how I know :P
From my 747-400 manuals:
"Turning the Battery Switch off de-energizes the BCU Standby Power Relay (R7301), which provides a false duct overheat signal to the APUC. The APUC then shuts down the APU. Logic in the EIUs prevents false messages in this situation."
This autoshutdown has no cooldown period.