Took me a while (too long, honestly), but I got a working Conan Exiles Dedicated Server Docker image. I was about to give up on the project when the thing suddenly decided to actually allow connections (server started fine before, but errored out each time something tried to connect), so I ended up trudging on after all. The in-game or Steam server browsers don't find the server and I'm not sure why, but at this point I'm already happy direct connections work (at least from within my local network)
The documentation for the dedicated server is pretty much non-existent, wrong, outdated or a combination of the before and the logs are pretty useless as well. Shame they broke the supposed promise for a Linux version of the server as well, that'd have been a tad more convenient (and who voluntarily runs servers on Windows anyway?)
I'm now seeing if I can automate mod updates and then I'll probably throw it up on GitHub at least. As far as performance goes, eh, not sure yet, the load on my server doesn't go above 0.6 while playing which is still just fine. CPU also doesn't seem to particularly care, memory is a tad tight (can probably free some up rather easily) and some things in the game do feel laggy (eg. harvesting corpses). Will have to do some more profiling to see whether it's actually playable for more than just kicks.
In the event I do decide it's feasible to run a small server I intend to make public backups of the server database (well, accessible with the server password), this means that in case something happens (most likely some SteamCMD or Conan Exiles update breaking things) or performance does turn out unbearable people can download the database to their single player game and carry on (or host it elsewhere, of course). Server settings are not present in that database (something to be aware of when using something like Mikey's Toolbox to create and manage multiple single player games as well) but everything else is (player stats, buildables, etc)