Actually, it does. Fr. Geiger cites the Catechism of the Council of Trent in both his review and in his vlog. The specific reference is in Part I, Article II, under "Second Part of This Article: "Born of the Virgin Mary." Here's what it says:
But as the Conception [of Jesus] itself transcends the order of nature, so also the birth of our Lord presents to our contemplation nothing but what is divine.
Besides, what is admirable beyond the power of thoughts or words to express, He is born of His Mother without any diminution of her maternal virginity, just as He afterword's went forth from the sepulchre while it was closed and sealed, and entered the room in which His disciples were assembled, the doors being shut; or, not to depart from every-day examples, just as the rays of the sun can penetrate without breaking our injuring in the least the solid substance of glass, so after a like but more exalted manner did Jesus Christ come forth from His Mother's womb without injury to her maternal virginity. The immaculate and perpetual virginity forms, therefore, the just theme of our eulogy. Such was the work of the Holy Ghost, who at the Conception and birth of the Son so favored the Virgin Mother as to impart to her fecundity while preserving inviolate her perpetual virginity.