Yep
If you have the inverter charging the coach batteries the combiner will connect the two banks any time a charge voltage ( above the set limit is present ) on either battery bank .
So if the alternator is charging it should combine and charge the house bank from the chassis bank.
Or when the inverter is charging the house batteries it should combine and charge the chassis batteries
The same holds true of the solar if the solar charge controller manages to raise the coach batteries above the combiners threshold Voltage then the combiner should connect the to battery banks and everybody gets charged.
I'm not to sure the Echo charger works in both directions but I know the Magnum battery combiner does it also has a provision to allow you to use a solenoid to give the system higher current capabilities on my coach I connected it to the boost solenoid to achieve this feature.
Eric