Only the player themselves can tell whether or not the Champion of Cyrodiil is the Nerevarine or not, though it is hard to explain that one would lose all their ability gain from being the Nerevarine.
Well, that could potentially be explained, but it would take some thought to come up with a plausible explanation, I mean, your items could have just been taken from you when you were sent to prison, but losing all your skills and attributes wouldn't be quite so easy, I'm also not sure what happened to the Nerevarine's corprus disease, I mean, at the end of Morrowind, while the negative effects of corprus disease are gone, you still have the disease immunity and presumably the long lifespan as well, and I don't believe that something happened to remove that too. Still, if you want them to be the same character, I supose that as long as you can adress any oncinsistencies that might create, you can decide whoever your characters are. But I don't think the canon Nerevarine and Champion of Cyrodiil are meant to be the same person, most likely, it is as we've heard, that the Nerevarine went to Akavir. Why? What did the Nerevarine do there? Is he still there? Did he even make it there? These we don't know, but we can probably assume the Nerevarine did indeed go to Akavir.