Do any denominations officially teach that Adam and Eve did not have the opportunity to be saved after they sinned?
Jehovah’s Witnesses do not believe there is any biblical basis to think that Adam and Eve could benefit from the ransom sacrifice of Jesus, which means they believe they will not be resurrected. This is what they say on page 49 of their ‘Bible Teach’ book:
“Clearly, then, when Adam disobeyed God and was condemned to death, he paid a very high price. His sin cost him his perfect human life with all its blessings” (Genesis 3:17-19)... There was no hope for Adam or Eve because they wilfully chose to disobey God.”
Here are some other direct quotes from their literature:
Watchtower 1 May 2005 article Who Will Be Resurrected? “15 The first humans, Adam and Eve, were created perfect. Their fall into sin was deliberate. Before them was either everlasting life or death. They disobeyed God and sided with Satan. When they died, they had no prospect of benefiting from Christ’s ransom sacrifice. Rather, they went to Gehenna. 16 Adam’s firstborn son, Cain, murdered his brother Abel and thereafter lived as a fugitive. The apostle John described Cain as one “who originated with the wicked one.” (1 John 3:12) It is reasonable to conclude that like his parents, he went to Gehenna when he died.”
Watchtower 15 July 2005: Questions from Readers – Who will be Resurrected? “The Scriptures speak of only two possibilities for the dead—the temporary state of nonexistence and the state of eternal death. Those who are judged unworthy of a resurrection are pitched into “Gehenna,” or “the lake of fire.” (Matthew 5:22; Mark 9:47, 48; Revelation 20:14) Among these would be the first human pair, Adam and Eve, the betrayer Judas Iscariot, and certain ones who died when God executed judgment upon them, such as the people in Noah’s day and the inhabitants of Sodom and Gomorrah.”
They believe that all who are in what they call a “temporary state of nonexistence” will be resurrected. This means everyone else who has ever died (prior to the battle of Armageddon) will be resurrected in a physical body to life on Earth and will have 1,000 years during the reign of Christ Jesus (from heaven) to come to saving faith. If they fail to pass the final test they will die (again), only this time they will suffer eternal death. They believe that all who die during the battle of Armageddon will (like Adam and Eve) forfeit the right to a resurrection.
Disclaimer: As a Christian of the Protestant persuasion I declare that I disagree with their views.