There is much to be considered here beyond just the tree of life and the tree of the knowledge of good and evil. We must first take a look at what happened when God created man in the beginning.
All Scripture is quoted from the King James translation.
Genesis 2:7 And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
Notice the part about becoming a living soul. The soul is an eternal part of man. Jesus himself gave us some insight into this in the book of Matthew.
Matthew 10:28 And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.
Here Jesus was referring to the second death, which we learn about in the Revelation.
Revelation 20:14 And death and hell were cast into the lake of fire. This is the second death.
And the soul of man will not be destroyed nor taste death until:
Revelation 20:15 And whosoever was not found written in the book of life was cast into the lake of fire.
So in answer to your question we cannot ascertain which any veracity
whether or not God intended them to have eternal physical life. However; we can without fear of contradiction most assuredly assert that God intended the soul to live for eternity. Which it will. All souls are in a state of waiting after physical death until the final judgment. At that time Jesus will judge all of mankind:
Revelation 20:12 and 13 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works. And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.
And since Death has already been cast into the lake of fire, the soul which are relegated to the Lake of fire will never die but suffer for eternity.
To my mind whether or not God intended that Adam and Eve and their posterity live a physical life throughout eternity is of very little importance. The important part to my mind is the eternal destination of my soul.
Those are my thoughts, you must come to your own conclusions.