Were Adam and Eve meant to live forever; had they not disobeyed God? In the book of Genesis we are led to believe that as God created man he was immortal.


  Genesis 2:17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.


Does that indicate that Adam and Eve and all who came after them would still be alive today had they not eaten from the tree of the knowledge of good and evil.
Yes.
As @Brasshat cites in his answer, Genesis 3:22 shows that to take from the Tree of Life allows one to live forever, and Adam and Eve were expelled from the garden specifically so that they could not eat from the Tree of Life and live eternally.
Messiah reveals in John 17 that to live forever means to know the Father and the Son, in the sense of familiarity.
It follows that had Adam and Eve not sinned, they would have had access to the Tree of Life and would have been able to eat continuously of the tree, and therefore have eternal life. The specificity of the reference to the Tree of Life in Genesis 3:22 suggests that it was God's intention for them to remain in the garden and continue to have access to the Tree of Life unless they sinned. Because they sinned, they were cut off from eternal life, and had no access to the source of life, which is the Tree of Life, and separation from the Source of Life is the death of which God warned them when he told them not to eat of the tree of the knowledge of good and evil.
So, because they would have remained in communion with the Source of Life if they had not sinned, they would have had life indefinitely.
According to Christian tradition, Messiah is the Source of Life. He says:

&quot;I am the true vine, and my Father is the Grower. Every branch in me that is not bearing fruit he takes, and every one bearing fruit he prunes, so that it bears more fruit&quot;
&quot;I am the vine, and you are the branches. The one who dwells in me bears many fruit, but apart from me you can do nothing.&quot;
&quot;I am the bread of life. The one who comes to me will not be hungry, and the one who believes in me will not ever thirst.&quot;
&quot;I am the bread of life. Your ancestors ate who knows what in the wilderness, and died. This bread, the one that descends from Heaven, whoever eats of it will not die. If anyone eats this bread, he will live into the ages.&quot;