A smart home can work without internet, but only for local features. Devices that connect by Bluetooth, Zigbee, or Z Wave can still control lights and sensors through a local hub. Many smart switches and thermostats keep their schedules and basic controls even when the internet is down. However, voice assistants, remote access, and cloud routines will stop working.
You also may not receive alerts outside the home. If offline control is important, choose devices that advertise local control and store automations on the hub. A stable home network still matters, even when internet service drops. You can also use physical buttons and schedules as backups, and keep manuals handy so the home stays usable for guests and family members.