I'd look into that closely. Sorry I didn't research your inverter and only reflecting on my system. Yours might be totally different in operation so you can take it at face value.
Myself I want total control of the charging. Maybe the unit supplies a 12vDC supply when plugged in? When I'm plugged in, my inverter becomes a 12v power supply and doesn't push a higher "charge" voltage into the battery system unless I switch it to a charge setting. In a sense with the charge switch in the off position, the inverter becomes a fully charged battery banked with the house battery system when plugged into shore power. I get enough from the solar that I figure I really don't need an additional charger when the van is sitting at home on the pad in most circumstances. I do set it to a charge setting from time to time but monitor the charge. There have been those Opps situations when I've left it on for several days... I try to avoid that.
In general batteries take what they need and is why chargers taper off when all is normal but you
can overcharge batteries especially if the charger doesn't have a temperature compensation feature or if a battery fails for some reason.
I'm not going over the hazards of an automatic charger overcharging a battery
again... only pointing out I've had a couple close calls. Much depends on how the inverter is set up and often there are ways to avoid what happened to me by using the correct settings.
Just know what setting can be programmed, how it operates, and understand the hazards.