It may, but its not the Jesus we know from the bible........just imagine all the things he supposedly done, like walking on water, raising the death and the rest, even when he died on the cross there was suppose to be an earthquake, and the graves opened, any many from the graves walked into the city preaching. Come on, if these things truly happened, they would have been writers about, not just by Josephus, but all the other historical writers of that time.
You might misunderstand what actually took place that formed the movement.
People wrote rhetorically and used mythology to build divinity in mortal men. They did it with the Emperor who was divine and the son of god before Jesus was even born.
He was not famous before he died, his death brought on his martyrdom in Hellenistic communities far removed from his life.
No credible historian follows the mythology, they follow the man who generated the mythology. Josephus is also not credible per say, we have only his biased view of the past. We don't take his words literally, but study to find out what has historicity in them.
Jesus did generate the mythology. Think about this, he took on the corrupt establishment by himself, if he rallied the whole Passover crowd , he could have overthrown Caiaphas and Pilate. But he failed, BUT his perceived selfless actions of a single man true of heart hit chords with some Hellenist, that is why he was martyred for his actions.
Remember while not really famous in Galilee, his actions in front of half a million people at Passover, made him the star of the show. Its my opinion that is what made an unknown Galilean trouble maker famous. The temple was corrupt and the Hellenist in control like Caiaphas were railroading the Aramaic Jews for massive amounts of money for Pilate. They were hated by all for this. Jesus may have tried to stop the money flow to Rome, he tried to make a change where others were cowards.
Teaching and preaching apocalyptic Aramaic Judaism in small villages will not make you famous.
Perceived selfless actions in the temple with half a million witnesses, can make you famous In a single day.
Either way because of his martyrdom, mythology was generated and it was taken home by those at Passover that lives all through the Empire. Each year they would return and share the good news, and the mythology grew and spread rapidly because of Passover and the huge gigantic crowds that came to celebrate.