Sin had entered into the world by one man, Adam. It took the last Adam to undo what the first Adam did. When He was sinless(I mean before He was imputed our sins, yet He never committed one sin), no one could lay a hand on Him to harm Him. After He drank of that most bitter cup, it was then, and only then, they could take hold of Him.
If the Christ would have lived to a ripe old age, would He have died? Here's the thing, we don't need to go by what if's but what actually took place. He ingested our sins, became sin, and died after He became sin.
The wages of sin is death, both physical and spiritual. That's why we are born dead in sin, and die later on. Through no effort of our own, we will die because of what Adam did.
And if they had eaten of the Tree of Life, eternal life would be through it and not the Christ. That was God's plan all along. That life eternal life would not come by eating from a Tree, but by eating from One who hung upon a tree.