All power supplies will draw a tiny amount of current when connected even with the cam turned off, but it would take at least a year to run your car battery down. Same for power control devices and circuits, whether built into the cam or external to it- they too will have a tiny current draw when not in use. With low-voltage cut-off, you should look for those having a range between 12.4V which is being very conservative, and 11.8V which is about as low as a car battery will tolerate when new. Most people seem to prefer 12.2V to 12.4V settings.
Phil