No. The Ting sensor is not powered by a battery, nor does it require a backup battery. Rather, the Ting sensor is plugged into a grounded outlet for power.
Should power be lost to your home, the Ting sensor will not function - but will resume functioning once power is restored, and will reconnect to your Wi-Fi once your router powers up.
Naturally, with no power in the home, there is no need for electrical fire hazard detection.