When Picard requests data from MusicBrainz there is more data sent than is made available as standard by Picard - Picard only extracts stuff that fits with standard tags.
But Track / Album metadata plugins can examine the data and see what else has been sent e.g. in the album or track artist part of the data.
Alternatively, like Album Artist Website plugin, you can run a separate query against an artist to get additional data which is not provided in the album web service response.
You would need to research and write a plugin for this.
P.S. Albums / Tracks can have more than one artist - so you might get more than one country. How would you want to handle this? Select the first artist, handle all artists?