I have a gas furnace for the entire house, and a gas fire place in the living room...?

If you have a gas fireplace then you have a chimney somewhere. The chimney might be inside the wall or the unit could vent out the back (if it's on an outside wall). If the fireplace is sealed (i.e., permanent glass between you and the flame) then it will probably have it's own intake vent and won't be drawing air from inside the house. Sealed units are reasonably efficient so yes, in that case, you might save a little money by turning down the thermostat if you're spending a lot of time in the living room.