The adapter is a transformer and will use some electricity when it's plugged in, if your lighter socket stays on when the car is off. Some do, some don't. My work van has two sockets. One turns off when the key is off, the other stays on. Try yours and see if the indicator light on the adapter stays on when the car is off. If so, I'd unplug it. It's not enough of a drain to kill your battery overnight or anything, but there's no reason to leave the transformer running, as they do wear out over time.