It sounds like a strange question. We think of Sacraments as perpetual signs that we partake of, yet Adam and his wife forfeited their benefit from the tree when they partook of the fruit from the tree of the knowledge of good and evil and were not allowed to eat from the tree of life. Let me admit that Scripture doesn’t specifically state that the tree of life was a sacrament but we may not be wrong to conclude that it was by “good and necessary inference.”
It helps to first answer the question what is a sacrament? A sacrament can be defined from Scripture as a holy sign and seal of the covenant (WCF XXVII; WLC 162; WSC 92). The sacraments are aids to our faith, presenting to our physical senses that which cannot be seen, namely a promise. Circumcision for Abraham both signified and sealed (Rom. 4:11) the promise of God to him. We understand that there is no magical power in any sacrament. Contrary to Roman Catholic theology, the sacraments of the New Testament do not work ex opere operato (that is by the working they are worked), rather their efficacy comes first from the institution by and the blessing of Christ as well as the working of God’s Spirit in the elect who receive them. The same may be said about any sign and seal given by God in Scripture (and I might add that some see a sign given for virtually every promise); for instance, to receive the sign and seal of circumcision was of no spiritual benefit to those who did not receive the promise represented in circumcision by faith – rather it signified their judgment as a covenant breaker who would be cut off from God and his people just as the foreskin was cut away from the flesh.
So when we come to the trees named and described for us in the Garden of Eden, we should not think of them as enchanted trees with magical power in and of themselves, but as signs to which God had attached the thing signified. Therefore to eat of the tree of the knowledge of good and evil was to partake in this knowledge and to eat of the tree of life was to partake in the life symbolized by the tree. Both knowledge and life find their source in God alone.
The tree of life was Adam’s goal. Had he met the requirements of the covenant of works he would have eaten for himself and all of his posterity from the tree of life and upon doing so would have gained and sealed the benefit symbolized by the tree for the whole race of humanity. But instead we find Adam barred from the tree (fenced from the table as it were) – deprived from the symbol and the life which it symbolized. He gave up the filet mignon for fast food. However, this barring was part of God’s covenant of grace which began with the promise of Genesis 3:15 after man had paraken of the forbidden fruit. Man was kept from partaking of the tree of life in his new condition of sin and misery that another may come and fulfill his covenant of works and bring man back to the tree of life in the New Jerusalem (Rev 22). It is amazing to me that this tree shows up again in the closing chapter of Scripture as a symbol, yes a sign and seal, of eternal life.