Alma refers to his previous discussion—the time between death and resurrection—and applies it to a past condition (Adam’s fall). Just as there will be a time between Corianton’s death and resurrection, there was a time between Adam’s expulsion and death. Here, this lapse of time is crucially important because it allowed Adam and Eve to repent. In fact, Alma argues that, without that space, they could not have repented.
If Adam and Eve had eaten of the tree of life, they would have lived forever—a condition that is part of the definition of resurrection. However, their earthly state could not have changed. For Alma, the resurrection (changing from mortal to immortal) symbolizes repentance (changing one’s spiritual state from sin to righteousness). Eating fruit from the tree of life would have short-circuited the plan of redemption, voided the need for an Atoning Messiah, and made them immortal but still burdened by sin. Alma seems to have in mind a poetic image of the atonement removing sin, just as death removes the mortal body.
Variant: The original manuscript had “put forth his hand immediately & partook of the forbi [sic] tree of life” which was corrected to “forbidden fruit.” “Forbidden fruit” was eliminated in the printer’s manuscript and all subsequent editions.