I have the stock converter and original batteries in my 2010. I leave it plugged in when parked, although care is required to be sure the water heater and electric heat are off.
The stock converter is not temperature compensated and will tend to overcharge batteries in hot weather. I check them every few weeks and add distilled water if needed, usually just once a year.
In cold weather, the stock converter won't fully charge the batteries, but it will keep them charged enough that they won't freeze.
To learn to see below the surface, you must adjust your altitude