If Adam and Eve had not eaten the fruit, would Jesus have been unnecessary?
The theological version of this question is: Would God still have become man in Jesus Christ if the Fall as described in the book of Genesis (Gen 3) had not occurred? In the light of the revelation we have been given by and through Jesus of Nazareth, the Anointed one (Christ), the answer is: Yes.
The mystery of the Incarnation of God in Jesus Christ and the resulting Salvation can be sketched in five steps.
I. Everything is created in and through Christ.
That which mankind has always yearned for and which each human being consciously or unconsciously hoped for has become true in Jesus Christ [...] in a unique way that exceeds all expectations. The heart of mankind is so that only God is large enough to fill it. This occurred once and for all through the Incarnation of the Son of God in Jesus Christ. In Jesus Christ the fullness of God was revealed (cf. Col 1:19) to fulfil and unite everything (cf. Eph 1:10)
The New Testament uses a variety of images and concepts to announce Jesus Christ as the fulfilment of time. In him the life and the light that always shone in the world is fully ablaze (cf Jn 1:4,9). In him the manifold wisdom and the everlasting mystery of God have been revealed (cf. Eph 3:9-10), so that in him all the treasures of wisdom and knowledge are hidden (Col. 2:3) In him God has brought everything together in the fullness of time and united everything in heaven and on earth. (cf. Eph 1:10) The New Testament takes this a step further: In him and through him all has been made. (cf. 1 Cor 8:6; Hebr 1:2; Jn 1:3). He is the first and the last (cf.) Rev. 1:17; 22:13
He is the image of the invisible God,
the firstborn over all creation.
For by him all things were created:
things in heaven and on earth,
visible and invisible,
whether thrones or powers or rulers or authorities;
all things were created by him and for him.
He is before all things,
and in him all things hold together. (Col 1:15-17)
[...] The early Church fathers frequently said that in all of reality, in nature as well as in culture, in the religions and in philosophy there are found traces, small seeds, fragments of the logos (reason, intellect, wisdom), that came to us in all its fullness in Jesus Christ. Therefore, Christ is the head and the fulfilment of all of reality (Irenaeus of Lyons). The Second Vatican Council says: Jesus Christ is the key, the centre and the goal of the whole human history (Gaudium et spes 45). In another place the Council says: The Lord is the goal of human history, the focal point of the longings of history and of civilization, the centre of the human race, the joy of every heart and the answer to all its yearnings (ibid 45). In particular, does the mystery of man take on light. (ibid) 22).
[...] So Christ becomes for the Christian the key to understanding the world and for the reality of living in the world [...] In Christ alone the deepest meaning of all reality is lit up. “Katholischer Erwachsenen-Katechismus” (German Catholic Adult-Catechism by the Bishops Conference), Vol. I, p. 164-165)
II. The Word became Flesh so that we can recognise God’s love.
“459 The Word became flesh to be our model of holiness: "Take my yoke upon you, and learn from me." "I am the way, and the truth, and the life; no one comes to the Father, but by me" (Mt 11:29; Jn 14 6). On the mountain of the Transfiguration, the Father commands: "Listen to him!” (Mk 9:7; cf. Dt 6:4-5). Jesus is the model for the Beatitudes and the norm of the new law: "Love one another as I have loved you" (Jn 15:12). This love implies an effective offering of oneself, after his example (cf. Mk 8:34).
III. “The Word became flesh to make us "partakers of the divine nature" (2 Pt 1:4)
For this is why the Word became man, and the Son of God became the Son of man: so that man, by entering into communion with the Word and thus receiving divine sonship, might become a son of God." (Irenaeus, Haer. 3,19,1) [...] "The only-begotten Son of God, wanting to make us sharers in his divinity, assumed our nature, so that he, made man, might make men gods." (Thomas v. A., opusc. 57 in festo Corp. Chr. 1). (Catehchism of the Catholic Church 460)
IV. This world, into which Christ has come, is marked by sin and by death
“397 Man, tempted by the devil, let his trust in his Creator die in his heart and, abusing his freedom, disobeyed God's command. This is what man's first sin consisted of (Cf. Gen 3:1-11; Rom 5:19). All subsequent sin would be disobedience toward God and lack of trust in his goodness.
398 In that sin man preferred himself to God and by that very act scorned him. He chose himself over and against God, against the requirements of his creaturely status and therefore against his own good. Created in a state of holiness, man was destined to be fully "divinized" by God in glory. Seduced by the devil, he wanted to "be like God", but "without God, before God, and not in accordance with God" (St. Maximus the Confessor, Ambigua: PG 91, 1156C; cf. Gen 3:5).
399 Scripture portrays the tragic consequences of this first disobedience. Adam and Eve immediately lose the grace of original holiness.(Cf. Rom 3:23). They become afraid of the God of whom they have conceived a distorted image - that of a God jealous of his prerogatives (Cf. Gen 3:5-10).
400 The harmony in which they had found themselves, thanks to original justice, is now destroyed: the control of the soul's spiritual faculties over the body is shattered; the union of man and woman becomes subject to tensions, their relations henceforth marked by lust and domination (Cf. Gen 3:7-16). Harmony with creation is broken: visible creation has become alien and hostile to man (Gen 3:17, 19). Because of man, creation is now subject "to its bondage to decay" (Rom 8:21). Finally, the consequence explicitly foretold for this disobedience will come true: man will "return to the ground", (Gen 3:19; cf. 2:17) for out of it he was taken. Death makes its entrance into human history. (Cf. Rom 5:12)
401 After that first sin, the world is virtually inundated by sin There is Cain's murder of his brother Abel and the universal corruption which follows in the wake of sin. Likewise, sin frequently manifests itself in the history of Israel, especially as infidelity to the God of the Covenant and as transgression of the Law of Moses. and even after Christ's atonement, sin raises its head in countless ways among Christians. (Cf. Gen 4:3-15; 6:5; Rom 1:18-32; 1 Cor 1-6; Rev 2-3. Scripture and the Church's Tradition continually recall the presence and universality of sin in man's history:
What Revelation makes known to us is confirmed by our own experience. For when man looks into his own heart he finds that he is drawn towards what is wrong and sunk in many evils which cannot come from his good creator. Often refusing to acknowledge God as his source, man has also upset the relationship which should link him to his last end, and at the same time he has broken the right order that should reign within himself as well as between himself and other men and all creatures.(Gaudium et Spes 13 § 1)”“
V. Christ became like us in all but sin.
Thus he reconciled the people with God and saved them, through renewing them and giving them a share in his own nature.
“619 Christ died for our sins in accordance with the scriptures" (1 Cor 15:3).
620 Our salvation flows from God's initiative of love for us, because "he loved us and sent his Son to be the expiation for our sins" (1 Jn 4:10). "God was in Christ reconciling the world to himself" (2 Cor 5:19).
621 Jesus freely offered himself for our salvation. Beforehand, during the Last Supper, he both symbolized this offering and made it really present: "This is my body which is given for you" (Lk 22:19).
622 The redemption won by Christ consists in this, that he came "to give his life as a ransom for many" (Mt 20:28), that is, he "loved his own to the end" (Jn 13:1), so that they might be "ransomed from the futile ways inherited from their fathers" (1 Pt 1:18).
623 By his loving obedience to the Father, "unto death, even death on a cross" (Phil 2:8). Jesus fulfils the atoning mission (cf. Is 53:10) of the suffering Servant, who will "make many righteous; and he shall bear their iniquities" (Is 53:11; cf. Rom 5:19). (“Catechism of the Catholic Church” 619-633). (see also the text introducing theme two: “Cross, Sin, Salvation”)