No BPS does not do this and since you should be moving your wp-config.php file to a Server Protected folder then you would have to do this from within your Control Panel or using SSH, depending on which web host you have. You cannot do this with FTP and you cannot do this with a plugin because a Server Protected folder can only be written too from either your Control Panel or SSH.
Or maybe there is an SSH plugin that will do this, but to be honest with you it would be silly to install a plugin that did this because you have to first enable SSH in your Control Panel and then you will probably only use SSH once.
IMPORTANT! If you do have to use SSH to do this then be sure to disable it after you are done.