Unfortunately Cloudflare have replied, and Plex very much is:
Hi there,
Thank you for contacting Cloudflare Support. We’re sorry to read that you’re experiencing difficulties.
We’ll actively discourage you from doing this, as it says in the terms:
2.8 Limitation on Serving Non-HTML Content The Service is offered primarily as a platform to cache and serve web pages and websites. Unless explicitly included as a part of a Paid Service purchased by you, you agree to use the Service solely for the purpose of serving web pages as viewed through a web browser or other functionally equivalent applications and rendering Hypertext Markup Language (HTML) or other functional equivalents. Use of the Service for serving video (unless purchased separately as a Paid Service) or a disproportionate percentage of pictures, audio files, or other non-HTML content, is prohibited.I dislike quoting T&C’s, to be honest, but that is what the system looks for, and triggering the usage you describe will cause everything to be routed off.
So if the traffic is running over the proxy, that will trigger the derouting for it all, even if it is not cached.
Sorry to be the bearer of bad news.
(REDACTED) | Cloudflare Support Engineer
So that clears that up. It seems people ought to stop recommending setups for Plex users on the forums (how I discovered CF in the first place!), as it could get them de-routed and/or their accounts terminated. 