Yes, the tracks have one embedded image marked "primary picture".
As a test I also adjusted (to no effect) ...
Preferences > Tags(1) > "artwork storage" > Set retrieval filter (button)
Even if not, then perhaps the first image found should be used as a default
Question: We have been arranging for the "primary picture" art.
MB downloads complementary hi-res large images and presents them in the ...
"Playing Track" main panel tab when the view is "Use MusicBee default layout"
and the following option is enabled ...
Preferences > Layout (1) > Configure Views (button) > Playing Track (tab) > artist photos
If "artist photos" is not enabled, MB displays a magnified primary picture.
Is this image data (which would make for wonderful wallpaper use) available via the API to you ?