Even though the camera has been set to take less than full resolution images from the menus, the image itself is most often (haven't heard of any other method yet) taken with the full sensor, and during the path from the sensor to the memory card, along with many other manipulation steps, the image is resized to its smaller size.
So yes, the image might seem a bit less noisy if taken as a smaller image, as each 'noise pixel' is sized down, but the image has to be made a whole lot smaller to effectively eliminate all noise when at its worst levels.
This applies to all digital cameras.