Always-Church and Physical Manifestation

From the "So-Called Second Letter of Clement of Rome to the Corinthians" (ca. A.D. 150) (as provided in Jurgens' Faith of the Early Fathers, Volume 1, at 43):

"I presume that you are not ignorant of the fact that the living Church is the body of Christ. The Scripture says, "God made man male and female." The male is Christ, and the female is the Church. Moreover, the Books and the Apostles declare that the Church belongs not to the present, but has existed from the beginning. She was spiritual, just as was our Jesus; but He was manifested in the last days so that He might save us. And the Church, being spiritual, was manifested in the flesh of Christ."

The proposition that the always-Church was spiritual throughout history until the incarnation, when it was made physically manifest seems contrary to my Reformed paradigm.

The Westminster Confession of Faith tells us that the Church before Christ's incarnation ("as before under the law") was "visible" only in one nation. Since then, it has become visibly manifest in all those throughout the world who "profess the true religion." WCOF, Chapter XXV, Sec. 2. I take this manifestation by profession to be a spiritualized manifestation; we are spiritually members of Christ's body, not physical members. While membership in the Church was through genetic lineage, a manifestation by descent, it is now passed on through the spiritual condition of professing the true religion. In other words, there is no more physical manifestation of the visible Church, only a spiritual manifestation.

Thus the Reformed view seems to be that the always-Church was physical (with the Jews) throughout history until the incarnation, when it was spiritualized for all peoples.

But the letter I quoted, thought to be the oldest extant Christian homily, does raise an interesting point. It would be an unusual irony if Christ's appearing in the flesh put the Church out of its own.