I don't see the relevance of the Gregory quopte. And apart from meaning you might have implied beyond the plain statement of Irenaeus, I have no disagreement.
Gregory's statement is made against the teachings of Apollonaris who taught that rather than having a rational, human soul and mind, this was instead occupied by the Divine Logos; and thus Jesus was a man inhabited by the Divine Logos in a way similar to how men have their soul and reasoning faculties.
Gregory's argument is that Jesus must be fully human, not just partly human, otherwise we have no salvation.
"Whatever is not assumed is not healed" means what it says.
Here is a fuller quotation, it is from the Epistle to Cleodonis, against Apollonaris,
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If anyone has put his trust in Him as a Man without a human mind, he is really bereft of mind, and quite unworthy of salvation. For that which He has not assumed He has not healed; but that which is united to His Godhead is also saved. If only half Adam fell, then that which Christ assumes and saves may be half also; but if the whole of his nature fell, it must be united to the whole nature of Him that was begotten, and so be saved as a whole. Let them not, then, begrudge us our complete salvation, or clothe the Saviour only with bones and nerves and the portraiture of humanity."
If Christ is not truly God and truly man, united in one undivided Person, then we do not have salvation. Our salvation comes from the One who, being eternally God, has united Himself to our humanity in its entirety (but without sin), in order that our entire humanity might be saved. For that which is united to His Deity is saved; anything that is not, is not saved. A Christology which denies the full union of Deity and humanity in the one undivided Person is a Christology
that denies our very salvation.
That is also what Irenaeus says in the quoted portion. It is the union of the Divine with the human that redeems the human. God, become man, suffering, dying, rising for our benefit; for that which we are united to what He is, in order to redeem what we are, and grant to us what He is and has.
Again, St. Irenaeus in his work against the Gnostics,
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but following the only true and steadfast Teacher, the Word of God, our Lord Jesus Christ, who did, through His transcendent love, become what we are, that He might bring us to be even what He is Himself."
Or as the Apostle St. Paul himself writes to the Romans,
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For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, 'Abba! Father!' The Spirit himself bears witness with our spirit that we are children of God, and if children, then heirs—heirs of God and fellow heirs with Christ, provided we suffer with him in order that we may also be glorified with him."
And the same Apostle says elsewhere to the Galatians,
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I mean that the heir, as long as he is a child, is no different from a slave, though he is the owner of everything, but he is under guardians and managers until the date set by his father. In the same way we also, when we were children, were enslaved to the elementary principles of the world. But when the fullness of time had come, God sent forth his Son, born of woman, born under the law, to redeem those who were under the law, so that we might receive adoption as sons. And because you are sons, God has sent the Spirit of his Son into our hearts, crying, 'Abba! Father!' So you are no longer a slave, but a son, and if a son, then an heir through God."
-CryptoLutheran