From its beginning, Plex has had a policy of not modifying your media files directly in any way, with the exception of deleting them in certain circumstances (which you have to enable). So I’m certain they are not writing tags back to your files. I, for one, would prefer it stay this way.
I’d like it if Plex would read and import embedded tags from photos as well. That’s a different request, and you should add your vote, if you haven’t already, to this thread.