Nah... you can only select subtitle BEFORE starting a movie. This detail must be fixable regardless of messy subtitle formats. I chalk it down to Plex being US centric, subtitles don't seem as important in that market I think.
This was a problem with playing some of my anime collection with EN dub and no subtitles. Now it defaults to JP dub and any available subtitles (99% of the time is only EN Subtitles, sometimes there are JP/CN and I haven't seen what happens in that scenario yet)