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
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.
And an American prototype:
All designs failed...