Maybe this will help.
I ran a shore power line from the dock that feeds a marine GFI receptacle I installed. Then I installed an on-board (Marine) charger that I plug into the GFI and I also run a dehumidifier in the cabin.
So with the GFI, I can unplug something and I have the option of running power tools or something else in the boat at the dock.
To your question I don't think a charger on the battery or batteries will keep up with the draw of a live well over a long period time. They don't put out huge amperage.
Maybe you can find an AC pump to just plug in at the dock to run the tank. I also thought of doing this, (someday). Or maybe a good size converter from the AC to DC and plug the pump right into it.
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