The capital sin of Sloth, according to St. Thomas, is "sorrow for spiritual good," in particular "sorrow in the Divine good about which charity rejoices." In other words, an act of sloth is a rejection of God's invitation to love Him because loving God seems like an oppressive burden.
(Of course, an "act of sloth" is primarily an interior act, since sloth as such inclines you to do nothing. In practice, what happens is sloth stops you from doing the right thing, then one of her daughters ("malice, spite, faint-heartedness, despair, sluggishness in regard to the commandments, wandering of the mind after unlawful things") prompts you to do a wrong thing. Devil's playthings, and all that.)
Given all that, it could be argued that the Rosary actually encourages sloth, since a lot of people say they find the Rosary wearisome, they despair of getting it right, they are sluggish in praying it, and when they do their minds wander (albeit not necessarily after unlawful things).
Let me suggest, though, that the Rosary can be a remedy for sloth (emphasis on "can"; it's not a magic spell), in different ways depending on how sloth is present in one's life.