Not so much.
What basis do you have for asserting that the Jesus of history 'bears no resemblance to Jesus in any way'?
All knowledge about Jesus comes from writings that originate years after his supposed death. So whether it's likely or not, his existence remains a hypothesis and must be treated as unknown till proven true.
The same can be said about many historical characters. If you are making the extraordinary claim that Jesus of the gospels was invented out of whole cloth then you have the burden of proof.
As for Nazareth the claim that it did not exist as an active town in Jesus' day is unsupported by the facts.
There are just too many convoluted stories in the gospels that make no sense if the writers had total freedom to invent a mythical character. Luke's contortions about the birth of Jesus is a classic example.