To prevent excessive drain when on the ground the Batteries disconnect if voltage is < 23 V for 16 sec. So leaving them switched on should not flatten the BATT's. Main BATT's have not connection to the APU as far as I am aware.
If both Batteries are AUTO, then the Batteries will supply:
1. AC ESS BUS
2. AC ESS GND
3. AC LAND RECOVERY BUS
NOTE: AC LAND RECOVERY BUS ignores the position of the Land Recovery Switch.
NOT Supplied:
1. AC ESS SHED
2. DC ESS SHED
3. SHED LAND RECOVERY