The traditional explanation is that a windmilling engine is robbing the gliding aircraft of energy, because of the power required to drive the engine against its friction and compression.
If an experiment shows that there is no difference, what is the explanation?
I have never tried stopping my engine (and never will) but I was once with an instructor who did stop the engine. It took a severe pitch-up; almost to a stall, to stop it windmilling. This was a C150. I don't recall how he restarted it.