Yes, you can always control all your lights directly from the device itself. If you have a schedule setup on a device it will run at the appropriate time as the schedule is stored in the device itself. If your home network is up you can control your lights from inside your home using the Wiser Home app. Alexa or Google voice integration will not work until the internet is restored.
Additionally, you will not be able to control your devices from outside your home network until the internet connection is restored. Please refer to the connected home offer for more details.
Do X Series Wiring Devices support copper-clad aluminum (CCA)?