Unless there's a mechanical relay in the converter to disconnect the output, then the output is connected all the time to the 12 Volt system.
I suppose you are correct.The relay would just open and thus disconnect when the converter is not powered.
I still wonder exactly what they are thinking by connecting the battery
as I described in my Scamp
I know with earlier converters there are just step down transformers and nothing else providing 12vdc and enough protection to keep things safe.
Although come to think of it in my Trillium
4500 there was a selector switch on the converter(transformer unit) to choose Battery
or Shore Power or Off.