I have a Growatt 6000T-DVM. I don't have solar, I just have 2 12.8kwh big batteries hooked up to it and I only have grid power for my supply. The way mine works, and I would presume all of the similar models they make do, is that it charges the batteries AND outputs AC at the same time. The inverter itself is getting power from the grid/AC input (unless of course there is a power outtage, then it's the battery). I don't think it's really drawing much current just to run the inverter itself, although I haven't verified. It does have a "power save" switch but I don't use that. Mainly because it's not even documented in the manual. The inverter is always "on", i.e. is always displaying the LCD screen. Unless of course I were to just move the switch to the off position. But then I also wouldn't be sending the grid AC back out to my load panel.
So for example, when I first got my batteries and they were basically empty and had to be charged, once my electrician hooked it all up and we flipped all the switches, all my devices in my critical load panel were getting their proper AC power and at the same time my batteries were being charged to the specifications I had set via the Growatt LCD panel's setup interface. It doesn't like only charge the batteries and then send AC out, it does them at the same time. Once the batteries got full, it stopped charging them and just simply routes the AC to the load panel. If I kill the master breaker supplying AC to my Growatt it instantly (instantly enough for my computer) starts grabbing power from the batteries and sends it out to your AC loads. Once I flicked the breaker back it switched back to grid in grid out and recharging the batteries at the same time. Not sure if that helps or not.