The answer
No. It is something that is not allowed, because it would mean a lack of respect for these sacred moments and would cause a distraction from the sacraments.
While Communion is taking place, the only other appropriate activity to be going on is the singing of chants or hymns of praise. So the Church should apply itself, at that point, to praising God for the blessings which He has poured out on us so lavishly, in permitting us to partake of His holy body and blood.
If we were to be distracted from the word of God by the words of other people, then this would be neither permissible nor
appropriate, because we would be neglecting the great. sacrament present on the altar, and would be giving our thoughts and feelings to the subject of the sermon.
Let us not forget that people usually listen to the sermon when they are sitting down, whereas during Communion it is not suitable for people to be seated.
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Thrice-Blessed Pope Shenouda III of Blessed Memory