Only if the issue is at the phone/app.The reader does get alarms though whereas, if the blue tooth connectivity with the phone is an issue, you won't get alarms on the phone even though you can still scan to get readings via NFC
"Bluetooth connectivity with the phone" has two parts - the transmitter on the sensor and the receiver on the phone (which the application accesses). It is not a simple case of the "Bluetooth connectivity issues with the phone" being a phone issue.
It is possible for the Bluetooth transmitter on the sensor to have a problem. If that is the case, you will not get alarms on reader or app but you can scan for readings on either (depending which you used to start the sensor, of course).
I am not suggesting this problem is the sensor or the phone or the app - without having access to either, we cannot categorically say. As an engineer, I know from experience, it is rarely worth speculating; only investigating.
And I am not suggesting one is better than the other - like so much diabetes related, we are all different with different preferences. I am just highlighting the impact of an Bluetooth error on a sensor.