All, I can say is I have read pretty much everything on the Romanovs and never heard of this, so it's news to me. I think that Alexandra would have had quite a few things to say about that document, because she was so committed to preserving her son's right to the throne.

Since there is no evidence of that, I would have to conclude either she wasn't aware of it ( unlikely) or it never happened. Did this person think Alexandra knew about it or not, and what about Nicholas? It sounds unlikely to me.
Sometimes people who teach history get caught up in either making it boring, or having interesting interpretations, which may or may not be accurate. This one doesn't sound accurate to me- and anyway, who would have drafted such a document? Nicholas? It doesn't sound like something he would do, and who could have done it beyond his back, because he was autocrat, even after the 1905 revolution, he still had much power. As well, until 1912, it wasn't really well known the Tsarvitch had had hemophilia, which you would have had to have knowledge of to do such a thing. I would not call a 1912 ( seven years after Alexei's birth) a few years, and anyway, what about the abdication, would not such a document's existence have come out then, or would Nicholas have kept it secret, and just signed Alexei's right away for other reasons, like he in fact did, that he wished Alexei to be with his family? He did say that was because of his illness, of course, and that was the main factor he considered. All in all, this sounds out there to me..