No, it's a link to their control panel from where they can edit their profile. There's no ajax, or in-line editing. I strongly believe that could and should be a core XenForo feature, and hoping to see it default in a future release.
- If the user browses their own page, they will see an edit link to edit their profile
- If the admin browses someone's page, the admin will see a link to edit the user's profile in the admin.php area.
- A .css file is included, for further css customizations.
- If someone wants this centered, just <div align="center"> .. </div> around the <a> .. </a> tags in the template.