Can a creation Light raise their own importance in narrative so that them dying causes a timeline to be doomed (like somehow ending up being hyperimportant in a number of loops)

This is literally something Aranea actually pulls off- She increases Jake’s relevancy in the story and forces his Hopey Potential out, forcing the whole scenario for Game Over, and her plan is to make the GO! Timeline so Relevant it overwrites the Alpha Timeline and ensures LE isn’t ever born. Which, of course, fails.