I'm sympathetic to the Jesus Myth theory, which I've written about a few times on Medium (links below). The version you're speaking of here was proposed by Joseph Atwill and James Valliant. I'm closer to Richard Carrier's version.
What's clear is that Judaism had to be neutered to survive after the war between Jews and Rome (compared to the zealous Judaism Robert Eisenman makes much of), and Rome shaped Christianity via Constantine's involvement in the councils. Christianity certainly syncretized Judaism and Greco-Roman culture. But there's a lot more going on in the gospels than Roman senators having fun. There's a transvaluation of the Romulus myth, for example, and a Judaization of the dying and rising god mytheme.