It's quite normal to shut down the single engine of a self-launching motor glider. However, in a 'Group A'(old term) aeroplane I personally think that it is crass stupidity to do so. And anyone who dangles the keys out of the window should be dangled out of the window themselves!
I couldn't find any reference to deliberate engine shut-downs in single-engined aeroplanes in the AIC concerning guidance to training captains conducting engine failure training - either the CAA cannot believe that any one would deliberately do so, or the topic is covered elsewhere?