Yes, he may have survived for another day, a week, months, or even several years despite what you and others think.
If there was even a hint someone was claiming to be Alexei, I bet the commmunists sent someone to make sure he wasn't the real Alexei. To them, this was politically important in the early years.
No, I don't think the claimants we know about were Alexei but that doesn't mean anything to me accept to prove there are people who out there who wanted to make people believe they were. And, that is sad

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If Alexei had suddenly poped up in England and knocked on the door of George V, do you think he would have been allowed in to see the King? And, what would it have taken, back then, for you and the rest of the world to believe he was the real Alexei? [Remember that was long before DNA.]
AGRBear