Well maybe if you fed the engine a stoichometric mix of O2 and fuel, and the main and tail rotors went round, I guess it would just spin at a rate proportional to the mass of the rotor versus the centre of mass behind the mast. ie damn fast.
And yet, and yet, as a way of re-entry, a ceramic rotor in autorotation to absorb the energy with a bit of gas thrust at the tail to compensate might just make an elegant arrival.
With a transition to the White House lawn, it would be very impressive...