Yes and no – the Plegium app must be open for the location text messages and phone calls to function, but it can run in the background and the phone can be locked. However, if the app is actively closed or "killed," it will not be able to receive the signal from the spray or the alarm button that it has been activated.
The Plegium device will automatically reconnect once the app is opened and it is within Bluetooth range of the phone. You can check the connection status in the app at any time.