We are all offered at mass indeed as part of His body:
Catechism #1368 The Eucharist is also the sacrifice of the Church. The Church which is the Body of Christ participates in the offering of her Head. With him, she herself is offered whole and entire. She unites herself to his intercession with the Father for all men. In the Eucharist
the sacrifice of Christ becomes also the sacrifice of the members of his Body. The lives of the faithful, their praise, sufferings, prayer, and work, are united with those of Christ and with his total offering, and so acquire a new value. Christ’s sacrifice present on the altar makes it possible for all generations of Christians to be united with his offering.
In the catacombs the Church is often represented as a woman in prayer, arms outstretched in the praying position. Like Christ who stretched out his arms on the cross, through him, with him, and in him, she offers herself and intercedes for all men.
Mary is also a
figure of the Church. Scripture tells us that in a special way, Mary would suffer with Christ:
Luke 2:34-35 Then Simeon blessed them and said to Mary…“a sword will
pierce your own soul too.”
Cross reference this with the birth of the Church:
Catechism # 766 “The origin and growth of the Church are symbolized by the blood and water which flowed from the open side of the crucified Jesus.”…the Church was born from the
pierced heart of Christ hanging dead on the cross.
Perhaps that sheds light on the article you linked to. Check the indented paragraph toward the bottom that has footnote 42 in it.