If there was no Rasputin, somebody else would fill his place. If Tsar wanted to be isolated from the events, he would find a way. There never is a shortage of shady characters preying on weakness of powerful people. Fact is Russian Empire was living on borrowed time by 1914. The regime was deeply unpopular, disconnected from reality and lacking any idea what to do beyond oppresing any and all oposition of regime. They were doing this in a cruel, yet inefficient way, that inspired revolt but did not come close to eliminating oposition in a way Stalin did. But, regime with the coruption so endemic that even in the time of struggle for its very survival some of bureaucracy would engage in blatant corruption had zero chance to survive any serious crisis. In short, no Rasputin or Rasputin, it stays the same, more or less. He just epitomized and brought to surface the worst things of the regime.