Another wonderful example of failed instructions and error handling. SharePoint seems to allow you to add the Enterprise Search Center, but it turns out that even though you can add the site template, it doesn’t actually show up when trying to create a site.
It turns out you need to activate a feature to allow you to actually create an Enterprise Search Center. Corey Roth has a post on this: Dude! Where’s my Search Center? So MSFT: Please only allow an administrator to select templates that are actually available!