Can a Mac mini connect to a Cinema Display 2009?

The answer is Yes! It may have some issues but it generally works.

Correct Answer by ToothpickProductions  on Aug 12, 2011 7:19 PM

Machines with Thunderbolt ports are still compatible with previous mDP models of displays, such as your 24″ Cinema Display.  You should be all good.

http://www.apple.com/thunderbolt/

(Just scroll down to the section “High Performance on display”