How do I get it to read that data? Do I need to run an import (via Sapphire) on that directory? If so, and if it pulls the data from the embedded metadata, how do I get Sapphire to import covers? Do I have to manually add them to the movies directory (like when Sapphire can't find a cover)?

It'll read that data when it sees a new file (such as browsing to the directory) or when you run an importer. When it imports the data, it should change the display name and the metadata displayed on the left. As far as cover art, you could submit a patch (Sapphire - Trac) to automatically pull it or put an image file in the appropriate location yourself: Collection Art

Also, for it to import the metadata, the .mov/.mp4 file must be properly marked as a TV Show or Movie in it's metadata (thought if you used a tool to set them in the first place, this is likely already set for you).