Even in the new heaven and the new earth man is not physically immortal, but has free access to the tree of life for healing that continuously imparts a form of maintained immortality.
Rev 22:2
In the midst of the street of it, and on either side of the river,
was there the tree of life, which bare twelve
manner of fruits,
and yielded her fruit every month: and the leaves of the tree
were for the healing of the nations.
Rev 2:7
He that hath an ear, let him hear what the Spirit saith unto the churches; To him that overcometh will I give to eat of the tree of life, which is in the midst of the paradise of God.
Rev 22:14
Blessed
are they that do his commandments, that they may have right to the tree of life, and may enter in through the gates into the city.
Yes, I think Adam would have died physically, if he had not kept eating from the tree of life to reboot his physical and genetic system as it aged.
Gen 3:22And the LORD God said, Behold, the man is become (Qal perfective) as one of us, to know (qal infininitive construct) good and evil: and now, lest he keep on putting forth (Qal imperfect) his hand, and-take (Qal waw-consecutive) also of the tree of life, and keep on eating (Qal waw-consecutive), and keep on living (Qal waw-consecutive) into an age/indefinitely ('L-oLaM).
I do not believe babies' spirits or bodies are corrupted at conception and at birth due to the effects of Adam's sin per se. I believe that babies are born in the same innocent state as Adam was made in, with the same propensity to wear out physically that access to the tree of life healed, and with the same propensity to be corrupted spiritually by temptations and lies so as to distrust God.
The consequences of Adam's sin stated in Genesis have become the burden of every human being. Spiritual death, as many imagine it, was not mentioned as a consequence of Adam's sin. Prohibition from the tree of life was a consequence, leading to inevitable death. Having to work for food by the sweat of his brow was mentioned as a consequence. Pain in child-birth was mentioned as a consequence. Spiritual death was not mentioned as an automatic consequence upon all genetic descendants. God communicated with Cain and Cain understood God . Enoch walked with God. The idea that spiritual death was inherited by all Adam's descendants, that we are born non-spiritual, is not taught in scripture as far as I can see. it is a misunderstanding of scripture begun with Augustine, because of his ignorance of Greek and his relying upon a Latin translation of the Greek text of Romans 5:12, and then eisegeted back into other texts to twist those to post hoc justify agreeing with Augustine's error.