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The Jesus Prayer referenced comes from believers within a structured liturgical tradition - principally the Eastern Orthodox Church - so there would be no connection with the use of the prayer in the sort of spontaneous manner that you suggest in worship. There is no use of the prayer in any of the eastern rite liturgies, for example (e.g. Liturgies of St. James, St. Basil, St. John Chrysostom). Although the prayer is said aloud communally within this tradition on rare occasions (e.g. there is one particular monastery in England that performs it in this manner), it is generally reserved for private, contemplative and usually silent prayer.