Dear Doctor John the Deacon,
Yes, indeed - Muslims often attend Marian feasts with the Copts and Ethiopians in Africa, and in other places where there are her miraculous shrines.
And they experience miracles through her intercession as well.
When Our Lady appeared at Zeitoun in Egypt in the late sixties, Muslims rolled out their expensive prayer rugs onto the sandy streets of Cairo and greeted the apparitions very devoutly (at least this is what I've read and heard from one of our parish priests who interviewed people there for a booklet he wrote on the apparitions - I have to be careful about sourcing things, Neil could be reading you know
And Muhammad did defend the Virgin Mary against the calumnies of the Jews of his day etc.
Archbishop Fulton Sheen once commented on this in a book of his that I read during a retreat with the Trappists of Oka in Quebec.
He said that he believed the Muslim devotion to Mary will eventually lead them to reassess their views of Christian doctrine.
All things are possible with God!