Like David, I'm not sure what you mean by "Connect switch". To my knowledge, the alternator will get the chassis bank up to snuff first, which shouldn't usually take long, then move to the house bank. The genset or park power (inverter sourced) will do the house set to something above 13v. then charge the chassis, as will solar. I welcome others more astute to correct me there, as different coaches can have different configurations, some a bit unlike my BIRD system.
If you mean by "Connect switch" the Coach Power at the entry door, aka. Salesman's Switch, that should not affect your charging scenario. You should not mess with that switch, by the way. It was not designed to be regularly turned on and off by owners, but rather for relatively brief dealers' convenience on sales lots. It and its solenoid have been known to wear inside and fail, and perhaps leave you in a spot sometime - been there done that, but was lucky I was in the BCS parking lot and the crew hadn't quite all left for the weekend. I was advised to leave that Coach Power switch in the "On" position 24/7/365, period. If you are storing the rig for awhile, turn its batteries off with the Main Switches in the battery bay, and never use the Coach Power switch. Mine get a constant solar input during storage (even with Mains off), but some people that store inside will disconnect battery ground cables to remove all parasitic drains including those from the electronic control modules not affected by the Main switches.
Regardless, once the alternator has your chassis bank up, perhaps within seconds, it will begin work on the coach bank. If you've been parked for long unplugged, the alternator will stress itself trying to boost 4 or more deeply depleted house batteries; the time involved at high charge rates can overheat it, deteriorating its components, and make for the most common cause of alternator failure. These commonly 160 amp diesel alternators aren't cheap, as you probably just discovered. The charger in your inverter, and in some cases one in the genset, are designed to do what the alternator isn't - deal with deep cycle house battery banks. Use the genset to recharge after dry camping or stored away from AC power - whether using its own built-in charger or feeding AC through the inverter's charger, your generator is more capable than your alternator. Plan ahead though; it can take quite awhile to get charged up before you dare start the engine to pull out on the road with minimal alternator stress.
On my rig I monitor the Magnum remote panel. After it has left the Bulk charge state, and gets into the Absorption phase where it begins topping things off and the batteries are around 90% charged, I like to see the charging voltage down to around 14.2 volts or less. That is the charging voltage, not necessarily the charge on the batteries, so as their state of charge comes up then the voltage required to pump current in should drop over time. Thus the charging voltage you see on your panel will slowly head down from maybe 14.6v to around 13.5v. The actual charge state of the batteries will be creeping up. Not long into the Absorption phase or Absorb Cycle is when I usually judge it relatively safe to start the engine and get underway. But as I said, it can take quite a long while to get to that point - maybe well over an hour - so plan your departure and start the genset accordingly.
Joel