If the Church's teaching on the Incarnation implicitly affirms that the conceptum is human from conception, then does the Church's teaching on the Immaculate Conception give additional witness to this?

It would seem not. Pope Pius IX's cites his predecessor Pope Alexander VII in the Apostolic Constitution, Ineffabilis Deus:

So at the instance and request of the bishops mentioned above, with the chapters of the churches, and of King Philip and his kingdoms, we renew the Constitutions and Decrees issued by the Roman Pontiffs, our predecessors, especially Sixtus IV,[8] Paul V,[9] and Gregory XV,[10] in favor of the doctrine asserting that the soul of the Blessed Virgin, in its creation and infusion into the body, was endowed with the grace of the Holy Spirit and preserved from original sin; and also in favor of the feast and veneration of the conception of the Virgin Mother of God, which, as is manifest, was instituted in keeping with that pious belief.

Later, Pope Pius IX gives the definition:

We declare, pronounce, and define that the doctrine which holds that the most Blessed Virgin Mary, in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ, the Savior of the human race, was preserved free from all stain of original sin, is a doctrine revealed by God and therefore to be believed firmly and constantly by all the faithful.

As far as I can tell, conception here is therefore identified with the creation and infusion of the rational soul into the body (as stated by Alexander VII), not with the fertilization of the ovum by the spermatazoa. I'd have to double check, but Pius IX does not offer a different definition of conception to replace that of Alexander VII. Hence, the apostolic constitution leaves open the question of whether conception, as defined here, takes place at fertilization.