hmmmm.... others should chime in here to help as I'm missing your logistics of how your system works.
though, if what you are assuming is that your Charger somehow 'uses' your batteries, then no, it does not, it has nothing to do with them other than providing 120v charging TO the batteries thru it's own controller... a Converter simply takes 120v incoming power and provides it to your 12v devices, such as lights, but NOT to your Charger or somehow to your Batteries. There is no 'circle' that you may be concerned with.
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