Willtor answered your querie so well I have very little to add besides quoting him.
Jesus is likened to vegetation on two major occasions. He is the True Vine and also the Tree and we the branches. That Tree is the Tree of Life, for He is our Life-giver, not just the bestower of our soul and spirit but also the bestower of New Life in Him and the Life Eternal that shall come at the end of this age. He was hung, don't forget, on a cross, which has always been likened to a tree, hence the cross itself is often called the Tree of Life as well, for it was His death upon it that made our salvation (and thus, everlasting life) even possible.
When we celebrate the Holy Eucharist, at least for us who believe in the Real Presence, we are partaking of the Fruit of the Tree of Life. That Blessed Food and Drink of His Body and Blood that nourishes our soul and our body, for it heals our soul and repairs our bodily nature, turning it from the sins of the flesh to things of Godliness.
The reason why God "hid" the Tree of Life from Adam and Eve is because they were no longer worthy. Remember what St. Paul says about those who receive the Eucharist without proper self-discernment? Same principle applies to Adam and Eve.
Adam and Eve were mortal (with an immortal soul, of course), and would have eventually been able to partake of the Tree of Life (Christ) had they not chosen to disobey God. If they ignored the serpent, I would hazard to say (although I wouldn't make a doctrine or dogma out of this) that it is possible that God would have allowed them to eat of its Fruit before their end, as a gift of their fidel, faithful service. However, I admit that is but a pious opinion, nothing more, for in reality, they chose to disobey God. That is why death is still among us humans; because sadly they lost out on the opportunity of eternal life for all of us.
Yet God had a plan for us to still partake of that Fruit, and He enacted it immediately, making sure all preparations were made before, in due time, He sent His Christ, that Fruit, for us. Now, He is here for us.
Let us enjoy the Wedding Feast! Praise the Body and Blood, broken and spilled for us! Amen Amen Amen!