I just finished updating all my files and tags and backups, (it took 6 days - 40 000+ files).
I had been under the impression since version 9.1 or 10 that with the "also store in files" checked, that the cover art was in fact being stored in the files as the tracks and images were imported, (I save the covr art images originally in the album folder, (next to file - not in the cover art folder). Alas, MC was only linking the image to the files and storing that in the database only. It seems that MC only stores the cover art in the file when you do an " update tags from library". It is not automatic, unless I have missed something.
If your cover art is already linked to the files in the library (db), then all you should have to do is highlight the whole audio library and the update tags from library. It will take some time if you have a lot of files.
If all your cover art is not linked, then you'll have to do that first as mentioned by marko. If they are saved in the cover art folder, your cover art should be named artist - album. (If saved in the album folder, MC 12 will rename the image artist - album automatically.). If the cover art is not named or linked, then you'll have to do that manually using the "add from file". Then update tags.
btw, updating my 43 k tags took about 12 hours, updating the 400gigs of backup drives took 4 days as nearly every tag had changed.