Yes. Moreover, it's dangerous historical revisionism to claim he had any role in the downfall of the Romanovs. Their embrace of him serves only to show how weird and detached from reality they were.
His influence was pretty minor and Communists probably could have taken over if he had died as a little boy.
Not just could have- would have. Things had been headed that way since the late 19th century at least.
Eh, I think that's quite deterministic. It's often forgotten just how small a minority the Bolsheviks were in 1917, so much so that their name, Bolshevik, the prefix bol meaning large, was meant to make themselves seem larger than they were in reality.
I agree that the Romanovs were probably doomed after 1905, but I don't think the Communists were the only, or even the most likely contenders to replace them.
Right, but that's not what we're talking about. If the only thing changing in the timeline is Rasputin, then everything else goes the same way.