The short answer is 'no'.
The app can be used on devices that only have a WiFi connection. The app only needs to have access to the Internet when you login. After you have logged in the app will cache all changes you make whilst there is no Internet connection available. When you next connect to a WiFi network, the app will sync all data in the cache with the web database.
The disadvantage of not using a mobile data connection is that the courier tracking will not be 'live' - you will have to wait until the device is next connected in order to view the tracking data in the web application.