it is quite logical to do so.
a talis godol is called in Halachah a “beged miyuchid l’Tefila” (which is why you dont bring it into the bathroom, although you do bring a talis koton into the bathroom).
nevertheless a talis is also used for kovod l’Tzibur. in many Shuls, for example, an unmarried male will put it on for opening the Aron, Hagboh, and Glilah.
My Rav always DAFKA leaves it on for his drosha after Mussaf, then removes it, although davening was over.
there is no Shabbos Shuva Drosha in my Shul, so i cant testify.