I too agree the best way to charge your deep cycle batteries when using the generator is to use the generator to operate your on-board converter which will charge the batteries. ALot of our smaller portable generatoes like the 2KW HONDA does a +BATT 12VDC SOURCE at a small 6-8AMPS DC which could trickle charge a battery when the generator was running but not does not have a good regulated DC VOLTAGE source to support any smart mode charging.
I am not up to speed on the larger wattage built-in RV ONAN GENERATOR but it may be the generator has an internal charging alternator type source to charge its CONNECTED START BATTERY when running. My SEARS LT1000 LAWN MOWER even does that ???
A quick test would be to measure the DC VOLTAGE with a multimeter on the start battery terminals before the generator is running and after the generator is running. The start battery terminals should read 12.6-7VDC if fully charged and after the generator starts up it should read around 13.6VDC...
Without smart mode charging techniques it will take 12 hours or so to charge up a deep cycle battery if it has been discharged to the 50% charge level.
Roy Ken