Do they already have MusicBrainz IDs in their file tags? There’s an option in Picard to “automatically scan all new files” and “ignore MBIDs when loading new files”. You will want to have at least the second one unticked if you already have MBIDs and don’t want them to be moved to the right-hand side automatically.
Note, however, that you can also drag the tracks from the right-hand side back to the left-hand side, so you can do the scanning.