Rob, as far as I know the unit continually senses any sideways movement, so will be "live" as such whilst connected to the car, unless it is powered through a switched relay that only supplies power when the engine is running.
In the write up there is reference to indicator lights on the A frame to confirm it is operational before setting off, but it does not say if the car is running or not.
If it is switched through a relay then it would be drawing no power when the engine is off, but if not, then it would be sensible to disconnect the 12s for a long ferry crossing.