On my motorhome, the combiner solenoid is activated from the "run" position on the key, so it does combine if the key is in run but the engine isn't running--the same situation where the fan blower operates, etc. (It is also activated by the emergency start button on the dash, which is actually a SPDT switch. When pressed, it connects the control wire of the solenoid to a house battery circuit; when not depressed, it's connected to a chassis "run" circuit.)
There are of course any number of minor variations on how these things are set up by different manufacturers and with different models.
