I doubt that the Church would have a problem with it. There are two groups of people who might be scandalized and/or offended – Catholics who do not understand and non-Christian Jews who do not believe converts to Christianity should be considered Jews after conversion. As to the first group, it is not a Christian’s place to tell a fellow Christian who is a Jewish convert that he cannot wear a tallit during adoration or the rosary. And it really shouldn’t cause scandal for him anyway since participation in adoration and the rosary is open to anyone, Christian or not, who wants to participate. The second group though requires greater consideration and tact since it is not fair to them to disregard entirely their self-understanding of Judaism and what constitutes Jewishness. I would simply say that a Catholic convert from Judaism should take care not to wear his tallit around Jewish family or friends who would be upset by the action. Some may not mind, of course; but those who do should have their sensibilities respected.
There is one more consideration for all Catholics to keep in mind. It is somewhat “fashionable” these days for Catholics to explore the Jewish roots of Catholicism (which is unobjectionable) and to indiscriminately take on Jewish practices and observances (which can be objectionable). Catholics who are not of a Jewish background should never presume to wear a tallit. Such an action would be gravely offensive to Jews, who believe that the tallit should only be worn by a fellow Jew. As to other practices and observances, I can only recommend that Catholics be very sure of what they are doing before presuming to, for example, hold a seder, wear a yarmulke, light a menorah, etc. Taking on Jewish practices and observances of any kind is a serious thing and not to be done merely because doing so seems “cool” or a “good idea.” If in doubt, don’t. It is far better to stick to one’s own traditions than to risk hurting and upsetting other people by indiscriminately co-opting theirs.