Yes, for the emergency alerts to activate, your Plegium device must maintain a Bluetooth connection with your phone within a range of 2-3 meters, and the Plegium app must be open. If you close the app completely, the device will disconnect and the app will not be able to recognize when you trigger it, meaning emergency alerts will not be sent out.
However, note that disconnecting a spray from your phone will not affect the other features of the spray such as the menthol spray, the LED light, and the siren. The spray will automatically reconnect once you open the app and it is within Bluetooth range of your phone. You can check the connection status in the app at any time.