Sending e-mails through GMail SMTP is possible. Just follow the steps described in the
Zimbra wiki. The SMTP Server name is smtp.gmail.com / TLS port is 587. The described approach brings you far. With the additional two changes, you will be able to send mail through GMail:
postconf -e smtp_use_tls=yes
postconf -e smtp_sasl_security_options=noanonymous
However, I noticed, that GMail is sending the mail under the name of the GMail account rather than the mail address of the sender...