(YouTube Link)
Swisscopter's Dragonfly is a small helicopter that has rocket engines on the ends of its rotors blades to propel them:
The copter makes use of tiny hydrogen-peroxide-powered rocket motors on the tips of the blades, which replaces the traditional engine-powered rotor. Large fuel tanks surrounding the pilot allow the Dragonfly to travel at up to 40 mph for 50 minutes.
via Popular Science | Company Website
It appears to be geared with the main rotor, but is likely pitched such that it doesn't provide any thrust to the left or right during flight. When the pilot wants to turn, he pitches the tail rotor blades to provide thrust.
If the tail rotor failed, the helicopter would be just fine, although it would have no ability to turn on its emergency descent.
actually it would start to spin uncontrollably with out the tail rotor, just because there is no powered axle between the main rotor and the main body of the helicopter doesn't mean that the friction from the rotor and where it is connected to the body isn't enough to cause it to start spinning. We don't live in a world with frictionless bearings. Also the fuel delivery system to the rockets probably add's a lot more friction to the main rotors axle.
It might not happen as quickly and violently as a normal heli would if it lost it's rotor, but if he were high enough, by the time he got the heli to the ground he could be spinning like a tea cup.
I like the noise of that thing- While most chopperbuilders work frantically on reducing or even cancelling the noise of their rotorblades as best as they can to make their choppers more useable in crowded areas, these guys come up with a system that wakes up the whole valley when they start up their machine. :-D
http://www.youtube.com/watch?v=8jhpUJLhQfs
http://en.wikipedia.org/wiki/Nederlandse_Helikopter_Industrie_(NHI)
And an American prototype:
http://en.wikipedia.org/wiki/YH-32_Hornet
All designs failed...
The difference with friction as a force is two fold. First, obviously, is that it would be in the direction of the rotors, not the opposite direction. Second, we're talking an incredibly small amount of the output of the engine being transferred via friction (easily as low as .01%). Third, it takes much more energy to spin the heavier body of the helicopter than the rotors.
So it would take very, very little to cancel it out.