Apple Configurator runs locally on an OS X computer. It requires a USB connection. So no ports required for connecting Configurator to iPads.
However, there are some ports that need to be opened for iPads to work with Apple's server if you are behind a firewall. Here is a list of known TCP and UDP ports used by Apple software products: http://support.apple.com/kb/HT6175?viewlocale=en_US
To use iPads behind a firewall (Configurator or not), you'll want to definitely open 5223 for Apple Push Notification and the standard ports for HTTP/HTTPS (80 and 443). If you're using an MDM, you will likely need to open 2195 and 2196 as well. If you still have issues port watch and see what an iPad does when trying to get to the store.
Hope this answers your question!