I dont personally think Rahul left the show to prevent Jasmine's exit. The way Big Boss has been this season, contestants get evicted or voted out any time and come back at their whims and fancies. Kavita, Aly, Nikki have all left in a just manner and suddenly come back. For Aly and Nikki, their comebacks were way easier and they werent even directed to difficult questions by a panel or Salman.
So Jasmine could easily have been voted out and brought back comfortably. Infact every contestant gets stronger after coming back. So Jasmine could have come back any time.
So Rahuls exit was either solely his act, that he thought this is genuinely the finale and Jasmine and Rubina may get more votes than him, hence lets make a clean emotional exit rather than being voted out.
Or Rahul's exit was orchestrated by Big Boss himself to rile him up and get him back on to the show to devote more to tasks.
But i dont think it was anything to do with Jasmine.