Risk from installing a "Nest" thermometer without shutting off home power?
Some systems are line-voltage in which case you could get a 120V or even 240V shock from the thermostat wiring.  I believe the Nest is designed for 24V systems.  It does seem a bit extreme to suggest turning off the power to your entire house.  I would probably settle with turning off the power to your furnace and then verifying with a non-contact voltage tester to ensure none of the wires are live.

On many thermostats, you can verify they are not getting power from the furnace by removing the batteries - if this display stays on, it's getting external power. If the display dies, then its not.

Always assume it's live until proven otherwise!