Local heating operation and radio-transmitter shutdown are different questions.
The UWG4 nSpire Touch WiFi can operate its heating system without a wireless-network connection. The manual explains that server connectivity enables remote control and weather information; these network services are unavailable without the required connection.
A disconnected or crossed-out WiFi indication establishes a connection status. The published manual does not establish that this status electrically powers down the WiFi chip or guarantees no radio transmission.
If the goal is simply to run heating locally, use the thermostat’s local controls and schedule without relying on app or weather services. If the project requires a thermostat without a radio, select a documented non-WiFi model suitable for the heating system rather than treating an unconnected WiFi thermostat as equivalent.
Source: UWG4 nSpire Touch WiFi manual (WiFi Settings and Troubleshooting the Wireless Network).