No, that's a completely unbelievable explanation. If he was fictional he'd not have been of Nazareth with a circuitous reasoning about why he was also of Bethlehem -- he'd have been directly of Bethlehem. His name wouldn't have been Jesus with a completely circuitous explanation about why "Emmanuel" also counts as his name, his name would have been directly Emmanuel.

These all seem to me to be false dichotomies, which assume that it's impossible either for a single creator to have embroidered their story as they went along, or for multiple creators or editors to have changed the story at different points in time.

Nor do I know of any fictional characters that are so deliberately placed recent history and yet their existence is believed by their contemporaries as real. If the Christian movement had began in the 1st century, and yet its founder placed as having lived in 3rd century BC, that explanation might make sense. But he was placed as a contemporary, and expected to be believed to be real. You don't do that with fictional founders of your order.

As long as it's far enough away in time and space that your claims can't be checked, what difference does it make? This seems to me like a post hoc justification for believing the Bible story, not an argument that anyone would have come up with if they didn't have a pet hypothesis to defend.

Also we don't have any evidence that Jesus' contemporaries believed he was real. The reports of people believing Jesus was real come from long after Jesus supposedly died.