The inverter/charger will charge the house batteries if you are plugged in or the generator is running. If the boost switch is on the house batteries and the engine batteries are connected and they will both get charged. If the power fails then both battery sets will get depleted.
A small charger will keep your engine batteries “maintained” when you are plugged in. Use the boost switch ONLY when you need all of the batteries to work together otherwise leave it off. Inexpensive way to keep the start batteries changed and extend their lives.
Boost switch which connects both battery banks via a boost solenoid. Advantage is it works quite well. Disadvantages are
The much better way is to use something that 'drains / directs' away some current from house batteries to keep start battery bank floated under a lower voltage with a limit on how much current start battery can draw from house bank.
There are several devices that allow this on the market. One of the most popular is Trik-L-Start (no longer accepting orders) Simply connect one wire to each side of boost solenoid or isolator and a third wire to ground. This device stays on all the time and boost is only used for emergency start of engine, etc.
A higher-end product that does the same thing is the Echo Charger. This is a popular device from Xantrex, a major inverter/solar, etc company. Echo Charger may have more features and the Xantrex is known for its good customer support.