Time clones from doomed timelines are indeed doomed eventually. But, what of Davesprite's case? A future Dave who should have been doomed went back, programmed himself into the kernelsprite, and was eventually programmed with Nepetasprite to become Davepetasprite^2. While fighting Caliborn with the Undertale reference, I don't recall Davepeta being defeated but I may be wrong. But now that the session is over and the game is complete, would Davepetasprite^2 still be doomed or no?

Davepeta is an entirely different entity connected to every version of their components and thus I feel that they are beyond that doomedness