for a given airspeed and collective pitch setting in normal flight, the whole rotor is rigged with the fuselague hanging beneath it, in the theoretical case of inverted flight, you would need substantial negative pitch over what is required for normal flight, plus as cran said, a stab aug system that would allow a fuselague to remain above it IMHO.
That in itself would be something probably more expensive than the helo. Yes, the RCs can do it, but I would like to see the hp/weight ratio compared to a helo.
It would be a most unnatural thing to lower the collective when approaching the inverted, ouch!