Prayer is more than words “said”. The Rosary is a beautiful and powerful form of vocal prayer (actually saying the words of the Our Father, the Hail Mary, the Creed, the Gloria), but it also is intended to lead us into mental prayer which requires us to ponder the words we say, paying attention to Whom we are praying, who is praying and what we are praying. We also need to ponder the mysteries of the Rosary. Before we even make an intention to pray for a person or persons, we need to recollect our own minds and hearts in order to pray with attention and devotion.
The Fourth Section of the Catechism of the Catholic Church is devoted to “Prayer” and I’d encourage you, if you do not have a copy of the Catechism to purchase one. See HERE
Your question it seems to me falls into the category of “How efficacious is your praying the Rosary?” The Catechism asks the question in Chapter Three, “The Life of Prayer”, in Part Four and gives answers:
How is our prayer efficacious?
2738 The revelation of prayer in the economy of salvation teaches us that faith rests on God’s action in history. Our filial trust is enkindled by his supreme act: the Passion and Resurrection of his Son. Christian prayer is cooperation with his providence, his plan of love for men.
2739 For St. Paul, this trust is bold, founded on the prayer of the Spirit in us and on the faithful love of the Father who has given us his only Son. Transformation of the praying heart is the first response to our petition.
2740 The prayer of Jesus makes Christian prayer an efficacious petition. He is its model, he prays in us and with us. Since the heart of the Son seeks only what pleases the Father, how could the prayer of the children of adoption be centered on the gifts rather than the Giver?
2741 Jesus also prays for us - in our place and on our behalf. All our petitions were gathered up, once for all, in his cry on the Cross and, in his Resurrection, heard by the Father. This is why he never ceases to intercede for us with the Father. If our prayer is resolutely united with that of Jesus, in trust and boldness as children, we obtain all that we ask in his name, even more than any particular thing: the Holy Spirit himself, who contains all gifts.
Mary our Mother asked the children at Fatima to pray the Rosary and we know that two of them have already been declared Saints. I encourage you to be childlike in praying for others and leaving all to God’s Love. Mary taught the three little shepherd children to pray after every decade: “O my Jesus, pardon us and save us from the fires of hell. Draw all souls to heaven especially those in most need of Your Mercy.”
Part of the quote from the Catechism I put in bold print, because those sentences seemed best to answer your questions. Hope these words are of some help to you. Thanks for asking!