No. And Yes. EpicTable works just fine off the internet. However, to play games online you do need to be connected to the internet.
What can you do if you're not? Many people, myself included, use EpicTable for maps and handouts even in face-to-face games. Read more about using EpicTable in face-to-face games.
Occasionally, I'm asked if people in the same location still need an internet connection if they're each using their own laptops. They do. This is because all EpicTable messaging goes through the internet, which allows it to just work, without any need to configure firewalls or routers.