No, in this scenario you will only receive glucose alarms¤ on the Libre 2 Reader. You can use the App to check your glucose, but you cannot receive glucose alarms¤ with the App because your Sensor was started by another device.

¤ Notifications will only be received when alarms are turned on and the sensor is within 20 feet unobstructed of the reading device. You must enable the appropriate settings on their smartphone to receive alarms and alerts, see the FreeStyle LibreLink User Manual for more information.