The Slavic churches do not do this; the Greek ones do. I don't know about the Slavic churches ruled by Greeks or the Greeks ruled by Slavs, or the Georgians who are neither Slavs nor Greeks.
I have never heard that inserted in ACROD parishes. From 'Come to Me', the English prayerbook of the Carpatho-Russian Diocese under the Ecumenical Patriarchate. (ACROD):
"Commemorating our ever-holy, ever-pure, ever-blessed and glorious Lady, the Birth-giver of God and ever-Virgin Mary, together with all the Saints, let us commend ourselves and one another and our whole life to Christ our God. "
The response is 'To You, O Lord' or in Slavonic 'Tebi Hospodi.'
The only thing close is the refrain found in the First Antiphon: "Through the prayers of the Birth-giver of God, O Saviour, save us." This, very clearly, is merely an intercessory prayer. Salvation is through Our Saviour.