Can I use 220V inverter as 12V power supply?
What you have sounds like an UPS (uninterruptible power supply).

The UPS have a charge controller that will detect the state of charge of the battery, so if no battery is connected and only some circuit, it won't work as the charge controller won't understand what is going on.

Although, you can connect a battery to it and then use it as a 12V power supply with the battery connected and this should work as the battery will keep a constant 12V (about) to the charge controller.