Restore is intended to be used in partnership with the app (which does require a Wi-Fi connection on both sides). That being said, your Bedtime routine and alarms, as they were originally saved in the app, will continue to run on your Restore without a network connection.
Keep in mind, Restore connects to 2.4GHz and we recommend connecting your phone to your 2.4GHz Wi-Fi band for optimal control of your Restore.