As you've mentioned, our Managed WordPress accounts have a special configuration. We do blacklist some plugins, but I don't think Backup Buddy is one of them. However, I can tell you that only your wp-content and database files can be changed. You won't be able to update core WordPress files, so deleting them from a Managed WordPress account isn't possible. You can access WordPress files using SFTP and the automatically created database using phpMyAdmin.
Managed WordPress has a built-in migration tool, which you may be able to use to pull in your site instead of doing it manually. However, if you still want to do it manually you can find some helpful guidelines here. Hope that helps!
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