Release notes for PMS 1.12.0.4829 state that the analyzer can now detect ATSC closed captions.
So, I’ve made two recordings, two different channels, with the Plex DVR.
Info (via plex web) of those files shows no closed captions.
The Apple TV client shows no subtitles available.
The Shield TV client shows no subtitles available.
However, Mediainfo says there are indeed closed captions in the file.
Furthermore, MrMC (and other Kodi like apps) can play the CC.