Im pretty sure that your batteries parasitic drag from inverter is only happening when AC is on , and not when DC ON andAC OFF, but wanted to be 100 per cent .
Thanks
Thats true as its the inverter that provides AC power. There is still some parasitic draw if the DC is left on as well, but much less than the inverter. I believe the battery pack voltage is around 58 VDC so it needs to be processed somewhat to provide 12 VDC and 5VDC to the DC side.