We Already Share in Body and Blood

Here's just one gem of many from today's Calvin reading:

But the flesh of Christ does not of itself have a power so great as to quicken us, for in its first condition it was subject to mortality; and now, endowed with immortality, it does not live through itself. Nevertheless, since it is pervaded with fullness of life to be transmitted to us, it is rightly called "life-giving." In this sense I interpret with Cyril that saying of Christ's: "As the Father has life in himself, so he has granted the Son also to have life in himself" [John 5:26, cf. Vg.]. For there he is properly speaking not of those gifts which he had in the Father's presence from the beginning, but of those with which he was adorned in that very flesh wherein he appeared. Accordingly, he shows that in his humanity there also dwells fullness of life, so that whoever has partaken of his flesh and blood may at the same time enjoy participation in life.

We can explain the nature of this by a familiar example. Water is sometimes drunk from a spring, sometimes drawn, sometimes led by channels to water the fields, yet it does not flow forth from itself for so many uses, but from the very source, which by unceasing flow supplies and serves it. In like manner, the flesh of Christ is like a rich and inexhaustible fountain that pours into us the life springing forth from the Godhead into itself. Now who does not see that communion of Christ's flesh and blood is necessary for all who aspire to heavenly life?

This is the purport of the apostle's statements: "The church . . . is the body of Christ, and the fullness of him" [Eph. 1:23]; but he is "the head" [Eph. 4:15] "from whom the whole body, joined and knit together by . . . joints . . . makes bodily growth" [Eph. 4:16]; "our bodies are members of Christ" [I Cor. 6:15]. We understand that all these things could not be brought about otherwise than by his cleaving to us wholly in spirit and body. But Paul graced with a still more glorious title that intimate fellowship in which we are joined with his flesh when he said, "We are members of his body, of his bones and of his flesh" [Eph. 5:30]. Finally, to witness to this thing greater than all words, he ends his discourse with an exclamation: "This," he says, "is a great mystery" [Eph. 5:32]. It would be extreme madness to recognize no communion of believers with the flesh and blood of the Lord, which the apostle declares to be so great that he prefers to marvel at it rather than to explain it. Institutes 4.17.9

If we as the Church already share in the Body and Blood of Christ through our union with Him, is it such a stretch to consider that in some mystical way we share truly and really in flesh and blood in the Supper of the Lord and not just in the Spirit? This is precisely the line of reasoning Calvin is following here.