The configuration.php file cannot be modified while backing up. It'd violate the principle of making exact clones which is the basis of backup software. You can, however, make sure that the database password is not included in the archive.
First, use the Files and Directories Exclusion to exclude configuration.php from the backup. This means that the entire file is no longer being backed up. This is not a problem since you're already moving your site to a different server and have to change all the settings anyway. Do note that you do not need to create one yourself on the restored site; the restoration script included in the backup archive will create one for you.
Then you need to go to Akeeba Backup's Configuration page, find the Database Backup Engine row and click on Configure. Check the box "Blank out username/password". This makes sure that the database connection information is not stored inside the installation/sql/databases.ini file when taking a backup.
Nicholas K. Dionysopoulos
Lead Developer and Director
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