The S3 operates comfortably without WiFi however data reporting, and over-the-air software updates may be affected.
S3 unit, individually, does not depend upon a network signal to operate. The S3 comes pre-enabled with Cellular data connectivity. In case cellular connectivity is not available in your facilities, S3 will rely on your Wi-Fi network to transmit data.
If there is no network, then the S3 would still detect and alert the operator however it won't send any data to the dashboard immediately so there won't be any email notification. Once the operator drives into an area that has good network coverage, the data will be sent to the Dashboard, and the notification will be generated.
Secondly, the software updates won't be pushed onto the devices unless they have a good connection.
In a nutshell, S3 needs a Wi-Fi or cellular connection to stream data to the cloud dashboard for analytics but that does not affect safety/operation.