If that's his reason, decreasing throttle achieves the same thing without the penalty of the 1-2 second engine start up delay. Quite frankly, IMO it's rather stupid to turn off your engine if you're trying to rope someone.
ack-ack
An idle engine still produces torque and thrust.
I have seen no proof of the efficacy or lack thereof in regard to shutting off the engine in the vertical to facilitate a hammerhead. If he thinks it works, so be it. I have no dog in this fight.
That said, a startup penalty is gamey in and of itself. With a windmilling prop reintroduction of fuel/spark results in an immediate relight in every recip I have ever flown.