…continue in the freedom of this covenant of life relationship which they had with God?
No. Adam and Eve, by their own decisions and actions, fell out of relationship with God by disobeying God. (Genesis 3:6-8, 13; Hosea 6:7; Hebrews 9:15) The serpent, described in Genesis 3 deceived Eve into questioning the goodness of God. After eating the forbidden fruit, she gave some to her husband Adam. Adam willfully took the fruit and ate it breaking the life covenant with God. (Genesis 3:1-13)
Moses finished the story of the fall by saying, “So the Lord God banished him [Adam] from the Garden of Eden to work the ground from which he had been taken. After he drove the man out, he placed on the east side of the Garden of Eden cherubim [angels] and a flaming sword flashing back and forth to guard the way to the tree of life.” (Genesis 3:23-24) In this Genesis account, God demonstrates both his character of justice and his character of mercy. Justice in that He judges disobedience; and mercy in that He makes his first promise of redemption as seen in Genesis 3:15.
Lest you think God did not like Adam and Eve anymore because of his banishment, it is good to see what God said to the serpent (the devil) before he forced the first couple to leave the garden: “And I will put enmity between you and the woman, and between your offspring and hers; he will crush your head, and you will strike his heal.” (Genesis 3:15) This is the first promise in Scripture from God that that he would defeat the enemy and save his children from their sin!
While sin has tainted their being and their actions, it is important to remember that mankind is still created in the image of God and so highly esteemed by God that he would save them rather than destroy them.