No such thing as an AC battery. What you have is some sort of power storage unit with its own built-in charger that converts AC to DC to charge the battery, and inverter that converts DC to AC to power your house. All this converting is highly ironic considering the main job of the power supply inside every component is to convert AC to DC. All our components run on DC.
You will get a lot more sound quality when this thing is disconnected from the grid. Then if you were able to regulate the DC and turn it into a DC power supply for each component, bypassing the components power supply stage, that would be another big bump in performance.
Sounds like a lot, but we are after all talking about someone who just dropped twenty large on a battery, and nonchalant about the same on an amp, so what's the holdup?