Right now my chargeverter is still in the box. I probably wont have time to install until next weekend. Think of the Battery BMS as a failsafe. You set the chargeverter to charge to a certain point, it should be less than the battery built in BMS. Your autostart (if you have one) using the dry contacts from the Inverter should be set to trigger well prior to the battery built in low voltage disconnect. If the battery BMS does a low voltage disconnect, in my experience you get a 6P code on the EG4 and it will not reconnect automatically, you have to reset the battery. This may be different if you are using the battery communication cables.
Using the chargeverter in my understanding solves a couple important problems. First, you have isolated the ac in from the generator the ac in is probably the weakest point of the inverter since it typically runs at the most current. Second, most generators are bonded ground/neutral I had allot of weird problems and some that were potentially dangerous when using the generator, including current where there should be none and GFCI breakers that would not work. I guess I could have removed the bond in the generator and maybe that would have solved it but there was also some issue with charging and powering loads at the same time. It just seems to me that running a separate charger and taking the job of ac based charging off the inverter was the logical move. Its what SS recommends for what its worth. This way the inverter is always running the loads off the battery - no bypass.