The term rheostat, tends to be an older expression that dates back to the days of using "windings" and a variable "wiper" to provide a variable resistance model between the supply and load, (light). With such a resistive device, the power consumption is actually increased slightly due to the additional component's presence in the circuit, but more importantly whatever power is not going to the bulb, is generated as "heat" at the windings.
In more recent years, we have moved to solid state devices which control the on/off time per each cycle of the AC current or a cyclic off time x times per second on DC current, but either way, the net result is a reduction of power consumption equal to the change in power factor, less a very slight amount of heat generated at the solid state device.
So yes, a solid state "dimmer" of recent and typical design can reduce the amount of overall wattage consumed for a given amount of light produced.
Keep in mind if you install a dimmer on the light over the stairwell and then fall down the stairs for not seeing the way, the medical bills may exceed the annual net savings from the dimmer. ;-)
In more recent years, we have moved to solid state devices which control the on/off time per each cycle of the AC current or a cyclic off time x times per second on DC current, but either way, the net result is a reduction of power consumption equal to the change in power factor, less a very slight amount of heat generated at the solid state device.
So yes, a solid state "dimmer" of recent and typical design can reduce the amount of overall wattage consumed for a given amount of light produced.
Keep in mind if you install a dimmer on the light over the stairwell and then fall down the stairs for not seeing the way, the medical bills may exceed the annual net savings from the dimmer. ;-)