The Smart Sock and Base Station connect via Bluetooth low energy. WiFi is only needed if you would like to use the app to view live readings and view them remotely. The Base Station is the primary notification system, so if your WiFi goes down or your phone dies (or you don't have it at all), the Base Station is still designed to notify. While WiFi is not required, it does make for a better user experience.
HotSpot WiFi is not recommended.