Initial email sent to admin@example.com

After a new installation of gitlab-ce_7.10.0~omnibus-1_amd64.deb, an email is automatically sent to admin@example.com which cannot be delivered.

$ postqueue -p
-Queue ID- --Size-- ----Arrival Time---- -Sender/Recipient-------
7183D4358A      663 Fri Apr 24 11:59:56  me@mydomain.com
              (connect to example.com[93.184.216.34]:25: Connection timed out)
                                         admin@example.com

Is this intentional behaviour? Seems a bit odd to me.

This is probably from your mail queue before you changed the admin email address.
This also happened to me. In my /var/log/mail.log I saw: (queue active) next to each entry for admin@example.com.

postsuper -d ALL

will delete all queued emails, as noted in http://www.cyberciti.biz/tips/howto-postfix-flush-mail-queue.html