No, The SkyBell does not have a back up battery.
The SkyBell is built to run efficiently off of low voltage wiring. The SkyBell must be wired to a constant source of low voltage power in order to view video and enjoy all of the other features.
There is a small battery in the SkyBell that helps the SkyBell distribute concise amounts of power to all the different components that run different features smoothly. This battery does not work as a sole power source, it is only to maximize performance and efficiency.
If there was to be a power outage in your area, the SkyBell would only continue working for a few moments. Once the power goes back on, the SkyBell will recharge quickly, reboot and continue to work perfectly as if nothing ever happened.
For now, this method of powering the device is the most efficient and allows the highest level of performance.