Could a quadrotor use a main gas powered rotor with small electric rotors for attitude control? Here is my idea of heavy lifting quadcopter. (Although it is not a quad copter anymore because of the center rotor)

Have a big coaxial fixed pitch rotor at the center. The rotor is gasoline fueled.
Have the other rotors at extended length with electric motors to control pitch yaw and roll.
The center coaxial rotor will do the heavy lifting.

Can it work? What are the difficulties?
Early versions of Sikorsky's VS-300 helicopter prototype used something similar to what you're describing, as his first attempts had three rotors on the tail boom, one vertical rotor for anti-torque and yaw, and two horizontal rotors for pitch and roll. 



Of course, if you're already using large main rotors, you might find, as Sikorsky found, that cyclic pitch control works even better and eliminates the need for the two horizontal rotors.