if you fired the extinguisher into the engine, the engine would suffer damage from the extinguishant that would render it good for nothing but scrap.
I think you have a misunderstanding here. The extinguishant (on every type I have been familar with) is not discharged into the engine, but into the nacelle or engine bay, outside the engine casing. There is constant fire inside a turbine engine - the absence of it is called a flameout. If there is fire in the engine bay or nacelle, you have a major problem, and that is where the extinguishing agent will go.
Does it wreck the engine? Not as much as a continuing fire would.