Allow me to rephrase the question in terms more suitable to the internet...
Whether God requires His creatures to have sex in order to condemn themselves?
Objection 1. It would seem that God does not desire His creatures to continually create themselves bearing the fruits of original sin, but is in fact happier with those whom he deigned to create or beget without sin. When God created Adam and Eve, sinless originally, He said that they were good (Gn 1:31). When God sent His messenger to Mary, sinless as she was, he said she had found favor with God (Lk 1:30). When God the Father spoke to His Beloved Son (also sinless) He said that in Him He was pleased (Mt 3:17).
Objection 2. Furthermore, God must need our participation to perpetuate Original Sin. Because without His creatures copulation, there would be no more Original Sin for Baptism to wipe away the effects of, thereby negating a vital sacrament of initiation.
Objection 3. It would seem that our nature inherits Original Sin because our nature comes from our parents. Since science might (today at least) have us believe that we had no tangible first human parents as evinced in the Bible by the persons of Adam and Eve, there could not have been two such parents to fall for us to inherit Original Sin from. Therefore cloned human beings would not be subject to the effects of Original Sin, nor would those who were not of the branch of Adam and Eve (let alone Noah).
On the contrary, Original Sin is a mark on the immortal Human Soul, created by God, for God and only from the Love of God. It is not sex that imposes concupiscence. So, No God does not require humanity's participation (though carnal unions or sterile cloning) to impose Original Sin on it. And yes, Original Sin will survive (thrive even) in a Brave New World. As Uncle Chestnut says:
Certain new theologians dispute original sin, which is the only part of Christian theology which can really be proved.
GCK - Orthodoxy
His proof for Original Sin, although tongue-in-cheek, will exist where ever humanity exists.
I answer that, this entire question could be swept away by the common Catholic teaching that the first 11 or so books of Genesis may be primarily useful in senses other than the literal
the first eleven chapters of Genesis, although properly speaking not conforming to the historical method used by the best Greek and Latin writers or by competent authors of our time, do nevertheless pertain to history in a true sense, which however must be further studied and determined by exegetes;
the same chapters, in simple and metaphorical language adapted to the mentality of a people but little cultured, both state the principal truths which are fundamental for our salvation, and also give a popular description of the origin of the human race and the chosen people. If, however, the ancient sacred writers have taken anything from popular narrations (and this may be conceded), it must never be forgotten that they did so with the help of divine inspiration, through which they were rendered immune from any error in selecting and evaluating those documents.
Pope Pius XII Humani Generis - 38
Pope Pius XII can concede nothing on the Spiritual and Everlasting Truths found in the first chapters of Genesis.
Reply to Objection 1 Although it can add nothing to His greatness, God is pleased by every one of our selfless acts of love and kindness. Otherwise He would not have said Blessed are they who... (Mt 5:1-12) Even though we suffer the residual effect of Original Sin (i.e. we have an inclination to sin) it can be overcame with the Divine Help.
Reply to Objection 2 Although St. Paul says that where sin abounds, grace abounds all the more. and during the Exsultet on Easter Vigil it is proclaimed "O happy fault, O necessary sin of Adam, which gained for us so great a Redeemer". It is clearly not good that we are borne into concupiscence and that is why Jesus is coming again one day. When we're borne into eternal life, we will be freed from that sinful inclination even though our souls were created and imbued with it. The Ox says:
Original sin is caused by the semen as instrumental cause. Now there is no need for anything to be more in the instrumental cause than in the effect; but only in the principal cause: and, in this way, original sin was in Adam more fully, since in him it had the nature of actual sin.
Summa Theologica Q.83 A.1 Reply to Objection 2
So, Adam had original sin, but it wasn't passed to him through his parent's sexual intercourse.
Reply to Objection 3 Although it is not clear whether anything besides children of Adam have human souls. Science has not the competence to trounce theology on the topic of human evolution (Youcat 42) Nor should theology inform scientific theory. The key point is:
Souls are not inherited Each is a distinct creation of God and is united with the body at the time of conception.
This is the faith - Canon Francis Ripley
There is nothing in science that can contradict this supernatural truth for this and many other reasons Pope Pius XII says
For the faithful cannot embrace that opinion which maintains that either after Adam there existed on this earth true men who did not take their origin through natural generation from him as from the first parent of all, or that Adam represents a certain number of first parents. Now it is in no way apparent how such an opinion can be reconciled with that which the sources of revealed truth and the documents of the Teaching Authority of the Church propose with regard to original sin, which proceeds from a sin actually committed by an individual Adam and which, through generation, is passed on to all and is in everyone as his own.
Humani Generis 37
Human nature is not strictly speaking a property of the human soul, the Rational Immortal Soul is God's gift to human nature. Aquinas and Aristotle teach that everything has a nature and a soul. But the powers of the human soul vary considerably with those of the rocks and fishes but the danger is that they can suffer the effects of Original Sin and even if there were no women left on earth, each cloned man would still be limited by whatever God determined the powers of his soul would be imbued with. In this case one needs to interpret literal inheritance or can posit a sideways inheritance in Paul's writings. But in the absence of a test for a soul in those who we hope would be naturally having one, it is impossible for science to know whether cloned individuals would likewise have or not have a soul.