Changing the image path after images were uploaded
If I change the File Directory setting under the Field Settings will this break the paths of the files uploaded prior?

Yes

As i think you need to go a two step process.


Move the images to the new folder.
Update the existing image path in database.


Before moving with any process keep all the backups.

Refer these links which may help you to move

seeking advice on changing file system path after files have been upload

Moving the files directory