Can Plex be restarted when using it via Roku?

I haven’t had the same “broken left-menu” issue you’re describing, but others have been discussing it here, including a mention from Plex staff.

Plex Left Menu Requires Roku Restart - #18 by ljunkie

I’m not aware of any way to force-quit a Roku app. After they’ve been launched they exist in a “rapid restore” state, even if other apps have been launched in the meanwhile.

“System restart” of the Roku does appear to quit apps.