Fire Extinguishers in Aircraft
Wings, fire extinguisher systems fitted to aircraft are there to help save lives and airframes, not for any other reason. The last thing a pilot confronted with an engine fire would be considering would be the effect on the engine of using the fire extinguisher. As others have said, the extinguisher agent does not get injected into the engine, but into the engine nacelle. Additionally, when the Fire Handle or Fire Switch is activated, as well as arming the extinguisher system, all flammable liquids to the engine are shut off as is bleed air if applicable. As I said, the sole purpose of the fire extinguishing system is to extinguish any fire which occurs within the nacelle.