Does the Catholic Church urge people to pray by reciting, and prefer this method over praying by listening to or watching others pray? Is praying rosary by listening to a recorded audio track viewed as being as effective as praying by reciting the prayer oneself?
Note: by effective I mean effective for spiritual growth or, as we know the prayer affects spiritual battles, as influential in the spiritual realm.
St. Thomas Aquinas, in Summa Theologia II-II q. 83 a. 12 ("Whether prayer should be vocal?") c., writes:
Prayer is twofold, common and individual. Common prayer is that which is offered to God by the ministers of the Church representing the body of the faithful: wherefore such like prayer should come to the knowledge of the whole people for whom it is offered: and this would not be possible unless it were vocal prayer. Therefore it is reasonably ordained that the ministers of the Church should say these prayers even in a loud voice, so that they may come to the knowledge of all.
On the other hand individual prayer is that which is offered by any single person, whether he pray for himself or for others; and it is not essential to such a prayer as this that it be vocal. And yet the voice is employed in such like prayers for three reasons. First, in order to excite interior devotion, whereby the mind of the person praying is raised to God, because by means of external signs, whether of words or of deeds, the human mind is moved as regards apprehension, and consequently also as regards the affections. Hence Augustine says (ad Probam. Ep. cxxx, 9) that "by means of words and other signs we arouse ourselves more effectively to an increase of holy desires." Hence then alone should we use words and such like signs when they help to excite the mind internally. But if they distract or in any way impede the mind we should abstain from them; and this happens chiefly to those whose mind is sufficiently prepared for devotion without having recourse to those signs. Wherefore the Psalmist (Ps. 26:8) said: "My heart hath said to Thee: 'My face hath sought Thee,'" and we read of Anna (1 Kgs. 1:13) that "she spoke in her heart." Secondly, the voice is used in praying as though to pay a debt, so that man may serve God with all that he has from God, that is to say, not only with his mind, but also with his body: and this applies to prayer considered especially as satisfactory. Hence it is written (Osee 14:3): "Take away all iniquity, and receive the good: and we will render the calves of our lips." Thirdly, we have recourse to vocal prayer, through a certain overflow from the soul into the body, through excess of feeling, according to Ps. 15:9, "My heart hath been glad, and my tongue hath rejoiced."
Two simple answers to your question, but first some recent papal encouragement to pray the Rosary:
If the Pope insists on the recitation and meditation of the Rosary, it is because he knows the Church and mankind are facing great dangers, like the threat of a world war and the attacks against the family, that can only be stopped “through an intervention from on high.” As the Holy Father wrote: *“The Church has always attributed particular efficacy to this prayer, entrusting to the Rosary the most difficult problems. At times when Christianity itself seemed under threat, its deliverance was attributed to the power of this prayer, and Our Lady was acclaimed as the one whose intercession brought salvation. In Her many Apparitions on earth, like in Lourdes and Fatima, the Virgin Mary always recommended the recitation of the Rosary to obtain peace, and to stop heresies. ”*
The Catholic Church encourages praying the Rosary, period. It's not an either or proposition regarding spoken or otherwise.
Insofar as spiritual growth effectiveness: No, not as effective unless prayed. (Experiential answer). I find it quite unsatisfactory, spiritually, to listen to the Rosary. Participation, either with a prayer group or praying the Rosary myself, is a far superior spiritual prayer experience.
As with many experiential and spiritual matters, this can and will vary from person to person. What the church endorses is praying the Rosary.
Insofar as your question on "effective" and "spiritual battles," the Church holds that praying the Rosary is particularly effective in that realm. See the details in the linked letter, where you will see abundant reference to the term "recitation" (and contemplation, and meditation) regarding this prayer.
