That’s possible. The body element will have a class indicating the current category that allows you to scope the theme easily using nested selectors in SCSS.
In general, I would recommend you to add a couple of Discourse widgets to the course area, like our supported iframe topic list feature documented at Embedding a list of Discourse Topics in another site. That way students can see a list of the most recent discussions related to their current course page and are a single click away to joining it in another browser tab!