Well, does one need to partake of the tree of life again and again to sustain physical life or is one bite enough?
It was in the garden for a reason, and Adam and Eve were told by God they could "freely eat" from it.. so, apparently, even in their perfect sinless state they needed access to the tree of life in order to live forever...
I think an interesting "what if" question would be "what if Adam and Eve never ate from the tree of Knowledge but also never ate from the tree of life?"
Would they have physically died in a sinless state? We know that is possible for Christ did just that.
The tree of the knowledge of good and evil had desirable fruit, that made Eve want to listen the the devil and eat that luscious looking fruit.
The tree of life, maybe the fruit did not appeal to eve or adam. Maybe they were not in the garden a long time for them to eat of that tree. Maybe they did not know where it was or what it looked like.
Perhaps they had not eaten of the tree of life because they felt no need for eternal life, not being dead yet.
They were not forbidden that fruit, meaning God's intention was to give them an eternal spiritual life, making them spiritually alive forever when they were ready to eat that fruit.
But they fell and God then said they were dust and to dust they would return, to the ground, from whence they came. So they died spiritually and were then susceptible to sickness and eventual death.
God in the prophecy told them of a savior to come who would free them from sin and death, being born of her, so then the savior would be made like unto humankind, so able to save us, being both human and divine, he would be our mediator between God and men, and He would crust the head of the serpent, signifying an undoing of the work of the devil which had resulted in their dying.
But God did not want them eating that fruit of the tree of life on their own initiative and abiility after they ate the other fruit, so He kicks them out and sets the angel to guard Eden from re-entry by any man.
God's plan was for Himself to show mercy and grace to people for fallen men to be saved.
Not for sinful man to be enabled to save himself by eating from the tree of life.
Man would need God's help to gain eternal life.
That way to eden likely remained guarded by the cherubim until the earth's destruction in Noah's flood. What a sight to behold for the evil men, likely they would have heard stories of that place.