Helicopter engines are designed to extract the maximum energy from the fuel burnt and send it to the gearboxes, with little left over at the tailpipe, maybe 50lb thrust.
Turbojet engines take as little as possible from the fuel burnt to leave it with more energy blasting out the back, i.e. thrust. Completely different designs.
And for a Chook to turn into a gyrocopter, the blades have to go from sucking air in at the top and pushing it down to generate lift and thrust (and being tilted forward), to then go to being tilted back and having air come in from underneath, and extract energy from it to stay up (autorotation mode). Again, a big jump to make.
With pusher props from another engine, and with stubby wings to provide lift, the rotors can be unloaded (not turned into gyrocopters), which just means it can fly with less collective lever, using less fuel.