Happily, Catholics do not mean the same thing by "predestination" that Calvinists mean.
Although we can't be absolutely certain of the state of our souls, there are signs that -- if we pay attention to them -- indicate which road we're on. For example, in his Dialogue of Comfort against Tribulation, St. Thomas More says that a life totally devoid of trials and tribulations is a sign of damnation, and that soon. And St. Alphonsus Liguori says that he who prays is certainly saved, and he who does not pray is certainly damned.
I take this promise of the Rosary in the same vein. It does not mean that we can do whatever we want, as long as we pray the Rosary; it does mean, I think, that if we are devoted to the Rosary, we are using a means provided to us to win through to salvation, and it will prove efficacious as long as we persevere in it.