A:Answer it draws power from your house. i believe the battery is just used for backup - if you try to install the thermostat without any power lines, it will throw an error and will not set up properly.
to answer your question: yes, you should have electricity running to the nest thermostat-e. i'm guessing your furnace doesn't necessarily need to have electricity running to it, but it needs to be controllable by your HVAC system to work with the nest.
check out the nest website for compatability: https://nest.com/thermostats/nest-thermostat-e/overview/#works/?mode=buy