Using the old wayback machine on my memory but if I recall.
In Theory, Anything using electricity puts a slight drain on the engine -
How -
As electricity is required by the car the alternator goes from spinning freely to being put under load to produce electricity, That spinning is done by the engine, so it adds load to the engine which causes it to use more gas.

So that is the theory - the fact comes into how much electricity an item requires. Rear Window Deicer uses a large amount of energy - The Radio, not so much (That is unless you have to power a sub woofer etc.. then it might be more)

So the amount of power required by your Radio is so small that it probably is not requiring any significant load, so go ahead and crank up the tunes!!