Bruce,
Energy is energy is energy. If you run an AC unit from an inverter or a genset, or if it is an engine driven compressor to get the exact same level of cooling requires the same energy. The only difference is in the efficiency losses between an alternator going through an inverter, or a generator's 120VAC output going through the inverter transfer switvch for example.
Assuming your coach regulator voltage set point is what you require based on your type of batteries, I would guess the inverter set point is higher by enough of a margin to effectively tell the regulator to shut off voltage output from the alternator.
Let me answer your previous Liberty question. How does Liberty do it? First, they do not run any house AC units from an inverter. If I want to run a Cruise Air while driving, I need to start the generator.
That in turn powers the Cruise Air, but also makes the inverters chargers. If the bus engine is running the inverters sense house battery voltage, and if the alternator is maintaining a charge on house batteries the inverter charging circuit is putting out minimal charging current.
If you switch your sense wire back to the chassis batteries but try to run a couple of AC units through your inverters at 24 volts your alternator will be putting out about 130 amps just to keep the AC units running. Add in other loads such as charging the chassis batteries to make up for the bus loads like daytime running lights , or to make up for other house loads like the refrigerator and you end up pushing the limits on the alternator. The greater the loads on it the hotter it runs and heat is the enemy.
If you add a second alternator it needs to be big enough so it is not run to its capacity or its life will be shortened.
If your chassis batteries are what your alternator senses (I recommend that) your house will receive the bulk of the charge if the house voltage goes down due to depletion frm AC units. The regulator will not be shut down by a higher inverter charge rate. But don't expect to get it all or for free. If you run AC units from the inverters you send power to the ACs from the batteries but the charge current going into the batteries may not prove adequate to maintain a full charge on the house batteries while they are under such loads. The house batteries and the chassis batteries will receive charging current to some extent however.
There ain't no free lunch.
I don't understand the concept of what you call over the road air. It must be a misnomer. My understanding of over the road air is a full coach Prevost system using a large engine driven compressor with large DC evaporator and condenser motors. With that system there is no need to run anything other than the engine, and it will freeze you out if set to max. The only time I ever need to run the generator while driving is if we want to run heavy loads such as the washer, dryer, other items not on the inverter powered circuits, including cruise airs (which we don't run while driving).