Actually, I think it is possible with the new “Plex Music” agent. If your tags are in as good a shape as you say, you should do well with Plex configured according to this guide.
When configured that way, Plex will use your local art files and embedded tags whenever possible, only backfilling from online sources when something is missing locally. That alone should be enough to do what you want. It will only look online if you’re missing something. But if you really don’t want Plex to even look for album art beyond your local files, you can use the “Album Art” setting, set to “Local Files Only,” to force Plex to not backfill missing album art, but it will still get Artist posters from online.
I’ve been configure this way for several years now, and it works really well, when my tags are correct. A side “benefit” is, you’ll find out very quickly, as I did, when your tags are wrong. 
One thing that came out of working with the “Plex Music” agent: You’ll be much better off if the embedded Album tag in your files is identical to the folder name containing the files. MUCH better off!
