No.

There’s lots of ambiguous information. There is no firsthand, historically agreed upon data that supports his existence in the form we know him today. In other words, there was no magical guy doing magical things.

There is no Roman record of “nailed 3 prisoners to the posts today; Bill, Roger, and Jesus the magic guy who was a pain in the ass.”

However, like Arthurian Legend, it doesn’t mean some guy like Jesus didn’t exist, or an aggregate of characters weren’t assembled to be him on story. Arthur was possibly just a chieftain of a group who fought a couple of hefty battles and made a name for himself, but he ended up being an almost magical figure with wizards and witches in the story and - guess what, he will “rise again” from the dead when needed. And no, rising from the dead isn’t owned by Christian religious figures, Osiris of Egypt did it, Dionysius of the Greek Pantheon among many others. So maybe some dude, who probably wasn’t named Jesus, caused a stir and got a few people to take note. That grew over hundreds and even thousands of years to what we have now.

Want to know why King Arthur isn’t a competitor to Jesus? He a) doesn’t offer the opportunity to control people in this life for the hope of an afterlife, b) he isn’t profitable.