I confess I rarely enter the boards dedicated to Alexei, but then I did a few days ago and I was thinking, what if? Being a doctor specialized in blood tranfusions myself, I was always somehow intrigued by the history behind blood therapy and a trigger point for it was certainly WWI. As a matter of fact, I remembered that the Soviet Union was somehow a pioneer in the field, although I never got the opportunity to find out more on this. So I looked it up and found out that even in the late 20's there have been Soviet doctors experimenting on various aspects of theories and possible treatments (Alexander Bogdanov to name one).
So, Rusputin is getting to be more and more an enigma, the way I see it, because in an alternative scenario, where the Revolution does not take place, or it does but the Tsar is non overthroned or anyway not killed with all the family, maybe a young Alexei would have the opportunity to be treated somehow. Of course he could also die as a consequence, since there were many factors, blood groups and compatibility issues that were not understood back then (Bogdanov's tragic end could be attributed to such an accident) - but again, who knows what could really happen, had Alexei had a decade or more to live?