Guess this one is binding.....
Thus as no man goeth to the Father but by the Son, so no man goeth to Christ but by His Mother.
ENCYCLICAL OF POPE LEO XIII ON THE ROSARY
http://w2.vatican.va/content/leo-xiii/en/encyclicals/documents/hf_l-xiii_enc_22091891_octobri-mense.html
The Rosary is a good practice, and Pope Leo XIII recognizes this, but nothing from a encyclical makes one’s salvation dependent on it.
You seem to think we act as Kantians under a Categorical Imperative, i.e. that a good practice, something that you would will everyone to do, becomes a moral imperative. That is not the case for Catholics. We don’t think that way.
We would do well to do what the Pope says, but we will not go to hell if we don’t. So no... not binding.