While it's true that the spiritual nature will dominate the resurrection bodies of believers, it is not true that we shall have no body at all. Even Jesus ate after He was raised from the dead (and Augustine questions certain interpretations of the Apocryphal book of Tobit which suggest that spiritual beings eating is only an illusion).
Again, the life-giving force in these bodies is spiritual, but that does not mean that they are not also physical in nature.
In the new creation our bodies will be made fit for heaven, but not unmade from being composed of earth. This change comes when we are grafted by grace into Christ as our new head.
Now we bear the image of the earthly man by the propagation of sin and death, which pass on us by ordinary generation; but we bear the image of the heavenly by the grace of pardon and life eternal, which regeneration confers upon us through the Mediator of God and men, the Man Christ Jesus. And He is the heavenly Man of Paul’s passage, because He came from heaven to be clothed with a body of earthly mortality, that He might clothe it with heavenly immortality. And he calls others heavenly, because by grace they become His members, that, together with them, He may become one Christ, as head and body.Thus we are changed from Adam's offspring and flesh into Christ's.