If anyone had survived, they would at least have had to make their family aware of their existence, which I am sure they would have wanted to do anyway, as this was the first acceptance, and the first connection to their old world whatever the life they had lived since. They would most likely have done that in a quiet and tasteful way, I agree, although inevitably when the news got out, hoopla would surely have surrounded them at least for a while, whatever they or their family wanted. They would have been a story, although it would have been much less if their claim was already proved, having been accepted by their family, etc.But would all the family have accepted a claimant, even one very authentic? Doubt always exists in some people's minds...
As for what they would have gained or what any imposter theorotically stood to gain, there was actually much. Succession rights, whether of much actual import, would have been at least a possibility. Obviously, the family was divided about who was the true heir, and might have been so in the face of a real claimant, but they could have put themselves out there. And, then again, there was the issue of whether there was much of a throne to claim. There was really only the title, the prestige, the tradition, as the Romanov dynasty wasn't going to be restored anytime soon. As for money, that was a very thorny issue, if there was any,etc. I don't think there was, but read William Clark's book on the subject for further info.Anyone claiming to be a survivor actually stood to gain, at least in the realm of theory. Some just wanted attention, which was surely to be gained. Others did believe they were that person, such as Anna Andersin for one. They had different motives. A true claimant would most likely just have been happy to have their true identity and family back, I think.