Since the cigarette lighter is always on and not connected to the ignition, can an USB charger permanently plugged in drain the battery and low long would it take to do it?

 

Only if it has something plugged into it and charging, otherwise its a negligible quiescent current, I have a fixed one with an LED voltage display, there is an on-off switch which I would use if I left the vehicle for a few weeks, the LEDS although infinitesimal probably consume more than the USB circuitry.

 

Unless of course the thing has a faulty component but then there would be smoke.