The onboard charger might shut off since it notices more amperage going into the cranking battery than it’s putting in.
Interesting scenario. But here’s what I know, along with some questions.
What size motor, and what is your alternator rated at?
Lets talk in terms of a 70 amp alternator. At idle, it’s probably only putting out say 10 amps. At WOT, it’s putting out it’s full 70 amps. This depends on what type of alternator it is. I’ve heard of some alternators that will put out the full 70 amps all the time. But I don’t know what those are and how that works.
I wouldn’t run both. You could wind up putting too many amps into the battery, and ruin or blow up the battery. Add a quick connect to the onboard charger port that goes to the cranking battery. Then if you decide to run a generator on the boat while running the motor you can just disconnect the cranking battery easily and still charge the other 2 batteries.
You could also put a switch inline on the positive cable and flip it off to stop it from charging the cranking battery.
Hope that makes sense.