It shouldn't; if it does, it is most likely that your browser is removing the trailing dot which makes it a FQDN.

Firefox's verdict:

> www.google.com. uses an invalid security certificate. The certificate is only valid for www.google.com

The fact of the matter is that FQDNs are probably only used in three ways:

1. By accident;

2. As a curio;

3. In complaints about how they don't work properly—badly configured server configurations, invalid HTTPS certificates, &c.

Works in Chrome 32, does not work in Firefox 26.