Hmmm...absolutely not. In fact, Revelation 20 enforces the teaching that the unredeemed with suffer the "second death", just as they suffered their "first death."
The question you are asking concerns eternal punishment, correct?
Correctamundo TD. As you say, the great white throne judgment described in Rev ch 20 is reserved for the unsaved who during their life on earth declined to accept Jesus Christ by faith in Him as their Lord and Savior. Since they declined to accept the gracious offer of Jesus to pay the penalty for their sins they will be judged according to their works in their earthly life. Which means that even one unlawful act or thought (Matt 5:28) will be found sufficient to disqualify a man or woman for eternal life and to consign him/her to eternal damnation in a place of suffering infinitely far from God's Heaven. IOW, they will be condemned to "the second death" because they refused God's free offer of eternal life through faith in His Son Jesus Christ and His atoning death in their place.
But, those who have been declared righteous by virtue of their belief in Jesus Christ as the Son of God in human flesh and in His resurrection from the grave, and have confessed Him before men as Lord have had their penalty for sin paid by Jesus' atoning death (Romans 10:9-10). And wonderful wonder of wonders, His perfect righteousness has been put to their account. Because of that, and only because of that, they will not be judged at the Great White Throne judgment. Their imputed innocence of all sin well be confirmed by the angel finding their names in the Lamb's Book of Life, and they will enter into God's holy city called Heaven to reside there forever.(Rev 21:27)
Read all about it y'all, it's in the Book that many of you have in your homes but never open.