You will initially need access to the internet on your iPad to add your event and download all the resources. Once you have started your event then internet is not mandatory. The system will simply queue the shares and photo uploads until the iPad has an internet connection again.
However, please note that if there is no internet connection then your guests will not receive their photos instantly but only once the iPad has an internet connection again and the photos are uploaded .
As mentioned, the system will queue the photos to be uploaded later if you do not have an internet connection but you will still need to have a network connection in order to print on-site. So your photos will only be sent out later when you connect to the internet but you can still print on-site.
What is the difference between internet and WiFi/network.