Would an aircraft with no ailerons, no elevators and no rudders be safely flyable?
An interesting thought. Control the aeroplane through its propeller(s), like a helicopter does. 


Propeller torque differential would control roll
Propeller cyclic would control both pitch and yaw
Propeller collective would control engine thrust, like already done in constant speed propellers.


The thing that immediately comes to mind is moment arm for pitch and yaw. Helicopter blades are relatively long, and the rotor is mounted about halfway along the fuselage. The prop is limited in its blade length due to ground clearance.

  

With a configuration like above, longer propeller blades can be mounted so the pitch and yaw moment arms can be extended. As @Sanchises points out, placing of the propeller like this creates a coupling between pitch and thrust - not a bad thing, increasing pitch controllability by controlling thrust. A strong nose wheel might be required for take-off.

Not sure about your reference to the skydiving Kamov, but the aircraft could glide down after engine failure while keeping enough RPM to control cyclic. It would be a bit draggy though, with the drag comparable with a parachute of the same diameter as the propeller. Autorotation works best with a large blade moment of inertia, and the propeller would definitely not have the optimal blade length for that.