Yes, the account definitely indicates that Adam and Eve would need to eat the tree of life's fruit in order to live forever. I would really like to hear a Witness try to explain this one. The ancient Jews did not imagine that humans could live forever naturally, as everything around them aged and died just like they did. Only divine intervention could halt the aging process, e.g. a magical tree.
My contention, personally, is that the story means to say that the fruit was something that needed to be eaten from continually to sustain their life, rather than a "one bite and you're immortal" kind of deal. This detail is not explained in the story, and ultimately it's unimportant. What we do know is that the cherubim and flaming sword were placed to "guard the way to the tree of life", not to ban Adam and Eve from the Garden as a whole (Gen. 3:24). This throws quite the monkey wrench into a theology that teaches that perfect man was immortal until his sin made him mortal.
But we can also go further and say that the word "perfection" is not found in this account either. It's true that man was better off before the fall, but the absolute concept of perfection seems to have been invented by Christian thinkers millennia later to reconcile the notion of a perfect God and imperfect creation (and we can also plainly see from the Bible's early accounts of Yahweh that the concept of a perfect God was also a later invention! One thing led to another).
All that the Eden story was intended to explain was:
- Why childbirth is so difficult, painful, and in former times often deadly, for human females when it's quite easy for animals (now we know the answer is the strong evolutionary pressure to develop larger brains while retaining bipedalism, which requires narrow hips -- both very desirable traits for our species).
- Why cultivating crops is so hard (it just is; the point of the story was that God seemed to have to account for why he made us to live by the "sweat of our brow" when he could have made life easier, the answer was that we did something wrong to deserve this life; well, our forefather and foremother did).
- Why people wear clothes, unlike animals (because we gained the knowledge of good and evil and became ashamed... this part is still kind of ambiguous, at least to me).
- Why men are in charge (God cursed the woman for her insolence by giving her a craving for the man, thus allowing herself to be dominated by him; this taken with the previous point implies that sexuality itself is a kind of evil knowledge, which in turn implies that the ancient writer thought that man ought to be higher in his mentality than the mere animals who underwent rutting and estrus).
- Why snakes don't got legs (they fell off due to a curse).
Any deeper meanings pertaining to absolute concepts like "perfection" and "immortality" are just eisegesis.