Is an additional rotor useful on a coaxial rotor configuration?
You could use the second rotor to provide anti-torque function only, as Arthur Young did when developing his helicopter test models at Bell during WW2.  In that case the upper rotor did all the lifting and the lower one had blades that were at 90 degrees and just made drag to generate a cancelling torque.

But that is really inefficient, and Young quickly moved on to using an anti-torque tail rotor (with a decently long arm to minimize the thrust it had to make), not wanting to go the whole-hog coaxial route, with all its mechanical complexity. 

So if you want to have a coax machine to do away with a tail rotor, you might as well design it so both rotors are lifting (to realize the efficiency you are seeking by going with co-ax in the first place) and you can easily get yaw control by using a mixing system operated by the anti-torque pedals that adds collective pitch to one rotor and decreases collective pitch to the other rotor equally, in a way that the total lift is unchanged but a yawing torque can be created and varied.  And there you go.