Absolutely. Mostly for exercise or to relieve frustration. I wouldn't expect a reduction in noise though.
As far as correcting the buzz goes, if this is still an issue for you, I would suggest checking out your "A" relay. This has a flip/flop switch that is NC and in it's off position, it energizes the right kicking rubber light. In the on state, it energizes the left kicking rubber light. This seems consistent with your symptoms. To reduce buzz in a relay, you need to reduce the load on the relay armature. You might try reducing the tension in the active blades or putting a lower force return spring on the armature. Also, your coil or something may be loose in the relay, causing the buzz. Another thing is that the coil may be tired and not able to put out the force it could in the past. Usually coils are either good or bad, but sometimes they get a little heat distressed and some of the windings get shorted. If the coil looks good, it probably is though.
If all of the above fails, try waiving a dead chicken over it.....or just live with it.