It's fer darn sure -you can't hurt the gas engines flooding em to stop.
just leaves more oil.
I shut em down after they have been idling and in looking at em later - there is a film of oil in em - I am paranoid about running over temp so I don't have any carbon build up . just shiny clean throughout
Power is not a problem as the tuned systems are run rich till they hit full tilt. then power maxes because the engine is not fully soaked with heat.
If your spinner is too hot to touch - you are fully heated ---------n then some