Yes, you can receive email alerts when AC power fails or is restored. Simply connect the sensor device to a mains-derived power source (e.g. a USB +5V power supply), and enable email alerts for AC power in Change Device Settings.
Caution: Readings may be affected on some types of sensor device while the internal battery is being charged. However, once charged, continued connection of the charger or external battery pack will have no effect.
NEVER CONNECT THE SENSOR DEVICE DIRECTLY TO THE MAINS.