How to apply the most efficient charging rate to a battery using a car alternator, in theory, paradise is when you start the engine and voltage immediately rises to 14.8 volts across the house battery terminals. Of course the voltage is going to decrease as the voltage regulator operates.
BUT BUT BUT BUT BUT
Many inverters TRACK
12.2 volts in, 115 VAC out
14.8 volts in, 138 VAC out
I would go right to the inverter engineering department and ask them "Does This Model Inverter Track Voltage?"
If they say "yes" or hesitate answering, then everything of mine gets disconnected when charging batteries via alternator or generator.
Some inverters may not "track". I have no idea which ones do and which ones don't.