As mentioned, the idea of flying inverted is probably only a hypothetical situation, but it does raise interesting aerodynamic considerations.
I believe (subject to correction) that in right-side-up forward flight the speed stability is achieved by the positive pitch moment of the rotor (flap-back) being slightly more dominant than the negative pitch moment of the fuselage.
Assuming that the rotor is capable of providing negative pitch and that the helicopter is flying inverted, will not the pitch moment of the rotor (flap- back???) and that of the fuselage both be positive (in respect to the horizon, not the helicopter). This seems to imply that there will be excessive speed stability and that the maximum forward speed will be very limited.