This could only ever be true for a fixed uniform static condition.
The important value is alpha. Anything that changes alpha independently invalidates the assumptions that the quoted relationship relies on.
Alpha can be influenced by any airflow changes perhaps due to translation or flapping so movement would cause changes independent of rotor speed. Then you have to consider that the rotor is inducing a flow itself and that with a real rotor this is not uniform.
In my opinion which I'm happy to be corrected on is that it is a far too simplistic. The real equation of lift for a rotor blade is not half.rho.v_squared.S.Cl, but needs to be integrated along the blade to account for changes in induced flow.