I believe the phrase from Genesis refers to ‘eat thereof and live forever in their fallen state.’ A man without God’s life in their human spirit is dead. A man with God’s earnest of the inheritance in his human spirit is alive forever more because God Life is unending. The ‘live forever’ relates to the ‘fallen state’, thus we know God made humankind to have unending existence, but without God Life in the human spirit, that living is comparable to being dead in trespasses and sins. Adam and Eve would be around in one form or another even beyond their physical bodies. Eating from the Tree of Life would have extended their physical lives unending, but in a fallen or godless state.
Rev 19:8 And to her was granted that she should be arrayed in fine linen, clean and white: for the fine linen is the righteousness of saints.Their nakedness signifies a lack of righteousness. Did God intend man to spend eternity in this condition?