They do. but some of them, if not all will die again before the thousand years is over, That is proved by Rev 20:6, where it says; if they do die again, their second death cannot hold them - as their names are in the Book of life and their immortality is certain, as they stand before God in Judgment.FYI again, Rev.20:4-6 says the beheaded Trib. saints REIGN with Him
No one is made immortal or removed from the earth before the GWT Judgment.
It is impossible for there to be immortals in the Millennium, with mortals. That would be a very strange situation. Only King Jesus is immortal until the worthy people go into Eternity.