The situation is covered in detail in another thread here. That is just an FYI, not an excuse for whatever they should be doing that they aren't.
BMS's generally cannot control flow in or out of a battery OTHER THAN by disconnecting the battery from the terminals entirely. So it is on/off in that regard. However, BMSs with communications features, when communicating with compatible chargers, can tell the charger what to do, and indirectly control flow in or out of the battery in that way.
The 100a Chargeverter does not communicate with BMS's. It simply tries to hit whatever voltage and current limits you set it to. Your batteries have recommended settings for charge voltages and current. You plug those in, flip it on, and don't really worry about it.
The only caveat to that is that lifepo4 do not like to fed 'charging voltages' for long periods when they are already full. With the chargeverter, you would need to notice when the charge current has dropped to 'tail current' levels (5% of your amp-hour number, generally) and turn it off. So, it would require some supervision, although only IF your batteries charge to full, and only WHEN they would be close to full. So if you do not use it to fully charge your batteries, you do not need to pay close attention to it. IF you DO use it to fully charge your batteries, and you know your starting point (state of charge), you can do some mental math to tell you how many hours until it would be near full, and only pay attention to it after that time has passed.
You could also power the chargeverter through a relay/contactor that is controlled by something else, such as dry contacts on your inverter, or an output from a programmable bms or 'battery monitor'. That would allow you to turn the chargeverter off automatically based on some conditions you could set up.
For example, you could use your inverter's 'switch from battery to grid' and 'switch from grid to battery' settings to control a contactor to turn the chargeverter on or off. If the chargeverter is powered by a generator and the generator is not running, nothing happens when you turn it on! So you could leave this control scheme working silently and doing nothing whenever the generator was not already running. However, when the generator WAS running, the inverter would turn the chargeverter off. This would let your inverter prevent overcharge but not start the generator without your permission. If your generator was able to be started and stopped remotely using the dry contacts you could have the inverter turn the generator on and off and leave the chargeverter plugged into it, in which case it is effectively controlling both.
All of that applies to any non-communicating charger or charge source.