Hmmmm, when googling I found this:
Powershield Commander 2000 VA Line Interactive, Sine Wave UPS
More a UPS than an inverter (2000VA/1600 watts). It looks that this type has an built-in battery
, one that will last for 30 minutes or so.
The specifications does not show a drain current
when not connected to a load. but if no other batteries are connected, I guess indeed your small internal battery
will be flat very soon!!!
Inverters of this kind of power can use 8 to 18 Watt for power when not 'used'.