The latest version of W3TC is broken and will mess up your Wordpress install. The latest update was released to resolve a known XSS vulnerability with W3TC but it has some pretty major bugs, one causing your site to respond with HTTP Error 500 for any request and even after you solve that issue the plugin is breaking libraries which are used for itself and other plugins.
That being said, I feel it might be time for EasyEngine to consider an alternative to W3TC. Viewing the update tracking log shows there has not been any active development since 10-dec-2014; all commits after that only change the compatibility of the WP version. The lack of development for such a plugin coupled with the most recent update breaking Wordpress to where the admin can't even access the admin panel, and sitting on a known XSS vulnerability till now is not exactly what I would consider a reliable plugin or company.
There are plenty of alternatives and I am sure at least one of them will make a better alternative to a plugin with such a bad track record as of recent.
I know you can simply select a different setup while creating a site but the default wordpress + nginx fastcgi_cache command also installs and configures W3TC; which currently creates a fresh wordpress install with errors and broken libraries. Even if it is decided to keep W3TC it would be nice to have an alternative fastcgi_cache option that doesn't use W3TC.