Yes. The tree of life in a certain degree was the cause of immortality, but not absolutely, because its effect was to strengthen the force of the species against the weakness resulting from the admixture of extraneous nutriment.
Lignum vitae quodammodo immortalitatem causabat, non autem simpliciter, quia habebat virtutem fortificandi virtutem speciei contra debilitatem provenientem ex admixtione extranei.
Yet it did not absolutely cause immortality; for neither was the soul's intrinsic power of preserving the body due to the tree of life, nor was it of such efficiency as to give the body a disposition to immortality, whereby it might become indissoluble; which is clear from the fact that every bodily power is finite; so the power of the tree of life could not go so far as to give the body the prerogative of living for an infinite time, but only for a definite time.
Non tamen simpliciter immortalitatem causabat. Quia neque virtus quae inerat animae ad conservandum corpus, causabatur ex ligno vitae, neque etiam poterat immortalitatis dispositionem corpori praestare, ut nunquam dissolvi posset. Quod ex hoc patet, quia virtus cuiuscumque corporis est finita. Unde non poterat virtus ligni vitae ad hoc se extendere ut daret corpori virtutem Durandi tempore infinito, sed usque ad determinatum tempus.
For it is manifest that the greater a force is, the more durable is its effect; therefore, since the power of the tree of life was finite, man's life was to be preserved for a definite time by partaking of it once; and when that time had elapsed, man was to be either transferred to a spiritual life, or had need to eat once more of the tree of life.
Manifestum est enim quod, quanto aliqua virtus est maior, tanto imprimit durabiliorem effectum. Unde cum virtus ligni vitae esset finita, semel sumptum praeservabat a corruptione usque ad determinatum tempus; quo finito, vel homo translatus fuisset ad spiritualem vitam, vel indiguisset iterum sumere de ligno vitae.
Wherefore Augustine says (De Civ. Dei xiv, 26): "Man had food to appease his hunger, drink to slake his thirst; and the tree of life to banish the breaking up of old age".
Unde Augustinus dicit, in XIV de Civ. Dei, quod "cibus aderat homini ne esuriret, potus ne sitiret, et lignum vitae ne senectus eum dissolveret".