Will 6th generation drain my car battery if left plugged in?

I would like to listen to music on my ipod nano 6th generation in my truck. I have a cord that plugs into my radio's input jack and into 12v power supply. If left plugged in 24/7, with it drain my truck battery. I left a radar detector plugged in for a few days while away on a trip and my battery was dead when I returned?

Thanks, Bob