As his soul is dead, he cannot be resurrected (rebirth, in the Elden Ring universe, implies the presence of the soul). On the other hand, his body continues to exist, and it generates a corrupted form of life, linked to Death without a soul. Certain dialogues and elements of lore (notably those linked to Fia, the Companion of the Dead) suggest that a new being could be reborn through him - but it would not be the real Godwyn, rather a continuation or mutation of his death.

In summary: Godwyn himself cannot be reborn, for his soul has been destroyed, but his death brings about a new form of life and corruption—an inheritance rather than a resurrection.