Yes, an internet connection is needed for your Kangaroo devices to work.
Specifically, a 2.4GHz is needed to be linked to your devices during the pairing process. The system uses it to communicate with the Kangaroo mobile app. If you're away from home, you also need mobile data to be able to receive push notifications for any motion detected.
Just in case your WiFi network goes offline, you will receive a push notification for it or an indicator on your devices within the Kangaroo App that your devices are offline.