Our app does have the ability to function without data (airplane mode, traveling abroad, no signal, etc.) if the device you are using has a native GPS chip. However, having a data signal (Edge, 3G, LTE) definitely increases the reliability of the recording. You will be able to track an activity and create a map by Recording.
The app does require a data connection for logging in, viewing maps and workouts (and other information within the app), and most importantly for saving recorded workouts. The app has a new local storage option that will save maps temporarily until you can find a data connection (cellular or Wi-FI), which should make it a bit easier to take advantage of the app in areas with low coverage or abroad.
If you do not have data then the app may not function correctly, especially if your device uses Assisted GPS like iPods, iPads, and other tablets. Also, unless you have Live Tracking on, the app only uses data when saving an activity or browsing your activity history.