Quoting from the Plane & Pilot article above:
We do know for a fact that performance can be really bad when you have a damaged prop. A survivor of a prop strike accident told us so. A Cessna 172RG was on an instructional flight out of the Washington Memorial Airport in Marthasville, Missouri, on April 23, 2002. The private pilot was killed, and the instructor received serious injuries. During a touch-and-go, as the plane was in ground effect, the nose suddenly pitched down, and the prop hit the runway. The airplane started vibrating badly, and the flying pilot turned the plane over to the instructor, who was unable to control it. The instructor told investigators that the airplane made a sharp turn to the left and went nose down into the ground.
On May 19, 2016, the propeller of a Beech D35 that was landing struck Runway 10 at the Gatlinburg-Pigeon Forge Airport in Sevierville, Tennessee. A witness said the landing gear had been up and, after the propeller blades struck the runway numerous times, the airplane skidded along until the engine speed increased and the airplane lifted off. The witness said the airplane appeared to be very unstable in ground effect, its performance dramatically deteriorated. It was observed to pitch up, roll to the left, and crash to the ground. The pilot, who was the only occupant, was killed.
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Please don't try to "save" an already damaged airplane. Ride the slide and live to tell the tale, even if you don't fly again afterwards.
How damaged is the propeller? What was damaged in the engine? Did your flaps drag down the runway, more on one wing than the other? How much power will the engine produce? What is your new propeller efficiency? You don't know. Maybe your controllable pitch propeller won't fully adjust, because the impact changed it's angle; maybe a tip broke off of one blade; maybe the crank shaft is cracked, and going for full power may break it.
Land the plane and live.