The Romulan agent in this episode directly references a sort of self-healing aspect to the timeline, like minor (Butterfly Effect) changes don't do the job due to .... something. As such, the presence or absence of that gun is probably indifferent to Khan's outcome.
Though one wonders if her speech to him might have reinforced the malignant narcissism that presumably underlies Khan's later cruelties.
True. For that matter, it could have just been that Starfleet time-cop group thwarting her over and over, without her realizing it.
Still, seems more like a lampshade thrown over the "temporal mechanics" here so the writers didn't have to deal with minutiae.