So this has been a useful debate.
We seem to agree that the rotor does not demonstrate one key feature of a gyroscope, namely rigidity in space. The question I think we're now trying to answer is whether the control lag for a helicopter rotor is 'like a gyro', ie. governed by the same kinematics as a gyro, or 'like a gyro' in the sense that it has similar observable characteristics but no connection to the kinematics of a gyro.
And then when we've answered that we can debate whether the gyro simile is an appropriate teaching tool for helicopter pilots. I would say that if the former prevails, then there's a qualified case for it. If the latter, then probably not.