If you run through the game without ever dying, saving or loading; does the game still refer to your timeline jumping abilities?
Spoilers ahead for Neutral and True Pacifist... Kind of.
If you go through the game without saving then things will happen depending on the route. If on a True Pacifist Route when it is supposed to say *You tried to save it will instead say *The only way to beat Asriel is to SAVE over his own file. But because you never SAVED before you don't know how. If on a Neutral route then before the Photoshop Flowey battle Flowey will mock you for having made no SAVE files but the battle will go the same, also at the end of the Neutral route Sans may make a joke about it and suggest you to save. The neutral route timeline will be lost after the game is closed but the True Pacifist run will secretly save itself to prevent loss. I don't know what happens on a Genocide route without saving although. Hope I helped.