No, they do not, but they do honor her foremost among the saints.
Catechism of the Catholic Church:
“The Church’s devotion to the Blessed Virgin is intrinsic to Christian worship.” The Church rightly honors “the Blessed Virgin with special devotion. From the most ancient times the Blessed Virgin has been honored with the title of ‘Mother of God,’ . . . This very special devotion . . . differs essentially from the adoration which is given to the incarnate Word and equally to the Father and the Holy Spirit, and greatly fosters this adoration.” — paragraph 971
“Mary’s function as mother of men in no way obscures or diminishes this unique mediation of Christ, but rather shows its power. But the Blessed Virgin’s salutary influence on men . . . flows forth from the superabundance of the merits of Christ, rests on his mediation, depends entirely on it, and draws all its power from it.” “No creature could ever be counted along with the Incarnate Word and Redeemer; but just as the priesthood of Christ is shared in various ways both by his ministers and the faithful, and as the one goodness of God is radiated in different ways among his creatures, so also the unique mediation of the Redeemer does not exclude but rather gives rise to a manifold cooperation which is but a sharing in this one source.” — paragraph 970
The Church rightly venerates the Blessed Virgin Mary as the first in honor among the saints, yet at no point is she ever worshiped. The worship of adoration is fitting for God alone is not shared with even the greatest of his creatures. Honorary devotion to the Blessed Mother fosters deeper worship of the most Holy Trinity, whose grace is at work within her. The Blessed Mother herself prophesied that ”All generations will call me blessed,“ as Catholics still do. Jesus kept the commandment to ‘honor your father and mother,’ and his Church does too. Click here to see Bible Verses relevant to the special honor that Catholics give to the Blessed Virgin Mary. Click here to see Bible Verses that are relevant to the saints interceding for us.