Sure! As an admin, you're unable to see any passwords in an employee's "Personal" vault. This is by design, so that user-specific passwords aren't visible to _anyone_ in the org except for that user.
However, this has a few downsides. All of those features I mentioned (alerts for re-used, leaked, weak, or old passwords) are visible to the owner of the private vault, but admins won't be aware of those issues. It requires trust and security training to make sure that those issues are handled appropriately for private passwords.
Also, if someone has edit access for a vault, there's no way to prevent them from moving credentials to their personal vault or exporting credentials. Most people won't know how to do that and won't bother... but it's always a risk.
