Is it true that anyone who prays the rosary cannot be touched by Satan?
Generally speaking it may be true, but it is not absolute.
Let me try to explain.
Praying the rosary is a great sign of predestination for those who pray the rosary with true devotion and love.
There are Our Lady's 15 Promises for Praying the Rosary, but we must recall to ourselves a simple fact:
These promises mean that, by faithfully and devoutly praying the Rosary, Our Lady will obtain for us the necessary Graces to obtain said promises. It is still up to each individual soul to respond to those Graces in order to obtain salvation.
Until we are in heaven we keep in mind that Satan and his Demons will always try to make us fall into sin and thus keep us out of heaven.
Signs of Predestination
Can we be certain in this life that we are predestined? In answer to this question the Council of Trent says: "No one, so long as he is in this mortal life, ought so far to presume as regards the secret mystery of divine predestination as to determine for certain that he is assuredly in the number of the predestinate; as if it were true that he who is justified either cannot sin any more, or, if he do sin, that he ought to promise himself an assured repentance. For, except by special revelation, it cannot be known whom God hath chosen unto Himself."14 The reason for this is because, without a special revelation, we cannot know for certain what depends solely upon God's free will. Not one of the just, unless it is specially revealed, knows whether he will persevere in the performance of good works and in prayer. We shall be, says St. Paul, "heirs indeed of God and joint heirs with Christ; yet so, if we suffer [perseveringly] with Him, that we may be also glorified with Him."15
Are there, however, any signs of predestination such as to give one a sort of moral certainty of perseverance? The Fathers, especially John Chrysostom, Augustine, Gregory the Great, Bernard, and Anselm, according to certain statements of Holy Scripture, pointed out several signs of predestination often enumerated by the theologians as follows:
1.a good life;
2.the testimony of a conscience that is free from serious sins and prepared rather to die than offend God grievously;
3.patience in adversities endured for the love of God;
4.readiness to hear the word of God;
5.compassion for the poor;
6.love of one's enemies;
8.a special devotion to the Blessed Virgin whom we ask every day to pray for us at the hour of our death.
Among these signs, certain ones, such as Christian patience in adversity, are proof that the inequality of natural conditions is at times more than compensated by divine grace. This is borne out by the beatitudes as recorded in the Gospel: "Blessed are the poor in spirit, the meek, they that mourn, they that hunger and thirst after justice, the merciful, the clean of heart, the peacemakers, they that suffer persecution for justice' sake: for theirs is the kingdom of heaven." These are the predestined. St. Thomas points out especially in his teaching that to bear patiently a heavy cross and for a long time is a sign of predestination. - What is a special sign of predestination?
As I have mentioned above that praying the rosary daily and with devotion will generally protect us from being touched by Satan or his Minions, but it is not absolute. Although we pray the rosary, we must truly pray and strive for holiness. St. Miriam of Jesus Crucified is an example of this. She is not an unique case either.
Even if we do all in our power to strive for perfection, Satan is always at the door try to find a crack to come in.
If God has permitted the saints to be diabolically possessed, how can we be absolutely sure Satan can not touch us? The saints pray the rosary. The saints are holy. Yet it happens in rare circumstances.
Saint Mariam Baouardy (St. Mariam of Jesus Crucified) was known for her devotion to the Blessed Virgin Mary and in fact was miraculously cured by Mary herself.
On 8 September 1858, Mary convinced him she would never abandon her faith; in response he cut her throat and dumped her in an alley. Mary lived, an apparition of the Virgin Mary treated her wound, and she left her uncle’s house forever.
She supported herself as a domestic, working for a Christian family and praying. In 1860 she moved in with the Sisters of Saint Joseph. Supernatural events began to occur around her, and the Sisters would not let her join their house. She was taken to the Carmel at Pau by a Sister in 1867, and became a lay sister. Later that year she entered the cloister, taking the name Mary of Jesus Crucified, and making her final profession on 21 November 1871.
She continued to experience supernatural events. She fought off a demonic possession for 40 days, received the stigmata, was seen to levitate, had the gift of prophecy and knowledge of consciences, and permitted her guardian angel to speak through her. Helped found the missionary Carmel of Mangalore, India. Returned to France in 1872. Built a Carmelite monastery in Bethlehem in 1875. Supernatural gifts aside, she was known for her devotion to the Holy Spirit, even sending word to Pope Pius IX that the Spirit was not emphasized enough in seminaries. - Saint Mary of Jesus Crucified
St. Mary of Jesus Crucified was a Carmelite Nun of 19th century and Carmelites are renown for their devotion to Our Lady and the rosary. Do not for the famous Scapular of Our Lady of Mount Carmel either.
Our Lady of Mount Carmel statue in Chile with a Brown Scapular