Mephis: the Romanovs would have survived at least a few years longer than they did because Russia wouldn't have entered WW1.
Russia's entrance into WW1 had little to do with the Russian Revolution. How Nicholas responded to domestic politics had everything to do with the Revolution. And that was influenced by Rasputin, right up until he was assasinated in 1916 by members of the Royal family.
Of course the historical accounts of pre-revolution Russia are controversial and much of what happened during those times has either been hidden or altered by the resulting takeover of Russia by the Bolsheviks. However, many historians attribute the fall of the Russian Empire to the interference of Rasputin in the internal workings of Russian domestic politics.
What I have said about the role of religious sects in Russian history is not legend according to several historians.