I think the question is whether sacred silence is being served, neglected, abdicated: that is, whether interior recitation of the rosary has the effect of making one more or less present to that particular moment of the Mass. (I trust it goes without saying that one would never attempt to have an interior recitation going on on top of the audible recitation of liturgy during Mass, if one could help it.) There has to be time in a liturgy not just for talking to God, but for listening.
I would think it better to know and concentrate on the liturgy actually taking place, but if it is necessary to recite antiphons to the Blessed Virgin and meditate on the mysteries of the rosary in order to keep one’s mind and heart where they belong, then that is far better than letting them wander. The intention and the effect would be the most correct possible. OTOH, if the devotion is in any way taking the place of the liturgy, or if the person was capable of meditating directly on the words of the liturgy or even the profundity of the silent actions taking place, then *it seems to me *that it is less than ideal to do anything else instead, including something as salutory as reciting the Rosary.
This is in no way meant to put down the Rosary, but to express the opinion that interior silence that is still fullly present to the Mystery taking place would be the ideal. If one can attend to liturgy and nothing but liturgy, not shopping lists nor schedules nor the annoying way someone is clicking whatever-it-is-that-they-are-clicking (!?!) in their pew, then that would be the best. If not, then to be bridled back into the correct moment by the Rosary seems a sweet mode of self-correction, and in no way something that would displease God.
In other words, I would think interior recititation of parts of the Rosary during silent portions of the Mass could be understood and used as a very good method of self-correction, but perhaps not the summit of presence possible, not the ultimate we would strive for in liturgical participation. Does that make sense?
If you have to have noises going on all of the time in your mind, after all, how is that different than having a dependence on physical noise going on in your ears? Not that the Rosary is noise, but I hope you know what I mean. You want time in the Mass where you do nothing but* listen*.