Using a Radiator Space Heater to Support HVAC system
Will using an electric space heater improve the efficiency of a heat pump?

No. When the temperature drops below the operational range of the heat pump, resistive heaters are used to provide heat. This would be the same as a space heater. However when the heat pump is running the heat pump is far more efficient at heating than a space heater. Depending on the model, some heat pumps can operate into the low teens, and a few models into single digits, but the efficiency will be the same when on electric heat (called auxiliary or emergency heat). The one difference is you can chose to heat only one room instead of the whole house with a space heater and that could save $.