Yes it does. Any electric/electronic device as long as the circuit is complete and electrons are flowing. Because energy neither can be created nor destroyed but converted to some other forms of energy. Example is the resistor with a semiconductor LED driving the power indicator of the AVR where electron flows to the material some are converted into light others are consumed by friction producing heat. The power supply of the AVR may come in a form of transformer where voltage is converted by induction, again not all energy are induced because there will be losses somewhere in the material and some in a form of friction=heat. The "plugged" equipment could also be using a small circuit for powering/snoozing the equipt.

If the fine print doesnt show current draw on standby use, one way of accurately measuring the consumption is thru the ammeter connected on the mains. A small computer AVR should be in milliampere range standby mode.