Could a rotor head wing be plausible? Could a helicopter support a detachable wing with no controls on top of the rotor head in place of a radar dome? Could the rotor head be made to support more weight? Would it be more fuel efficient at higher speeds, add a level of redundancy, or increase speed?  

I did consider clearance and the drawn pictures is not to scale. The wing may need to be drawn longer, further back or placed higher. This would be a payload in itself for extending the range of the helicopter under lighter loads. 

A second feature is that the wing could be made to catch the vortex left by the rotor blades in flight increasing air pressure under both the rotor blades and rotor wing. 

Similar to the way ducks fly in a v formation the wings would also take this advantage from other helicopters with this extra wing for extra lift.

Could extra lift be created from the rotor wing, the vortex ring redirection and /or flight in a V formation?
There is no need to attach the wing to the rotor head - simply attach it to the top of the fuselage. You could run the rotor through a hollow tube and attach the wings to that - the inner uncovered section of the wing is an interesting idea.

If you are looking for VTOL, a tilt rotor with two electric motors driven by the gas turbine may be a better option.