I guess to be pedantic, we're talking about sustained LEVEL inverted flight. Or better yet, can a helicopter maintain -gz?
Theoretically has been discussed, but practically I'd like to hear ideas why we'd want to do this. Other than airshows and kicks, the only purpose I can think of would be an agressive bunt for someone getting attacked. Maybe the Comanche can do this?
Interesting aside. 1996 International Helicopter Championships in Salem, Oregon (great time, outstanding hospitality). National title holding RC Helicopter aerobatics guy put on a show that I still can't figure out. Inverted flight quite common, but vertical dives with extremely rapid yaw rates, pointing nose down at ~10' AGL then pushing into an inverted hover at inches. WOW. Slow level flight ~6' AGL starts pitching 360 degrees while maintaining altitude and slow forward flight. No idea how this one works, must be some sort of illusion thrown in with exceptional flying skill.
Second show of day was cut short when 6" inverted hover turned into 0" inverted hover and $5000 helicopter turned into 5000 pieces. Talked to the guy afterwards. His attitude "part of the job". My attitude, "I'm not flying real helicopter inverted". especially at 6".