Rambam says in Igeret Teiman that Mashiach will live in obscurity until he is revealed as Mashiach. This would make the question a non-starter.If someone is universally accepted as Mashiach and does what Rambam says Mashiach will do (fight Hashem’s wars, build the Bet HaMikdash, etc.) he will be Mashiach.
Actually, there are are two. Mashiach ben Yoseph and Mashiach ben David. According to Kol HaTor of Rabbi Hillel Rivlin, one of the talmidei HaGra who made aliya,the job of the former is kibbutz galuyot and building the material side of EY whereas the job of the latter is building the spiritual side culminating in the Bet HaMikdash. Rav Kook (Misped b’Yerushalayim) apparently held that Herzl, or perhaps the Zionist movement in general, was MBY. He explained the anti-religious aspects as a result of his concentration on the material.