So you think if you had a radar detector plugged in....after 10 mins it would shut off?
Again, if the circuit it's connected to is designed to go to sleep after the 10 minute key off timer expires: YES. If the circuit is otherwise HOT at all times, the battery saver system would kill all unnecessary power after an extended period with no user activity (door opening, remote/keyless keypad button presses, etc.) if it felt there was sufficient power draw.
In my 2010 the cigarette lighter stays hot continuously and I know that because I have a back-up camera system installed and the screen standby LED flashes. I see it flashing anytime I look even if the car has sat untouched for days.
For those of you who haven't experienced it, I've had an alternator go out on my older Lincoln. As the battery voltage started dropping, the car would shut systems down to conserve power for essential systems: Radio, electronic climate control, mirror power, windows, cigar lighter, even the ABS system would be taken off-line. At that point I knew it was not going to stay running much longer, but I drove on rural roads and the highway for over an hour on a 1000CA battery, including a warm start.
In any case, would the LED pull enough to force the car into sleep mode: most likely not. However it's not just the LED if the detector is on, it doesn't care if the car is moving it is actively looking for signals to alert to, so how much power is the entire detector using 'at rest' looking and during an alert...