The only aspect of Golfshot which requires a network connection while you are at the couse is the downloading of aerial images.
Due to licensing restrictions we are not able to cache the imagery to your device which means you'll need a wifi or network connection for the imagery to download. On average this requires about 5 MB of data per 18 hole round.
The use of GPS does not require a network connection. If you don't have a network connection and the imagery doesn't download you will still have access to the GPS distances.