Nikon D600 D610 -- Can choosing a lower resolution improve the noise level?

Nikon D600 D610 -- I realize this is already a very low-noise camera, but I still have this question: Does choosing a lower resolution (before or after shooting) improve the noise level?

- Maximum / native resolution = 6016 x 4016 = 24.3 MP

- Next available lower resolution = 4512 x 3008 = 13.6 MP
- Next available lower resolution = 3936 x 2624 = 10.3 MP
- Next available lower resolution = 3008 x 2008 = 6.0 MP

For example, downsizing from 24 MP to 6 MP could be accomplished by averaging 4 adjacent pixels into a single pixel, (losing resolution but reducing noise).

Is there a setting on the camera that implements such averaging?

If not, can this be done in Light Room or Photoshop or other imaging software?

thanks for your answers

If the lower resolutions were obtained by averaging down the maximum resolution, wouldn't the noise level be decreased?

If the camera does not "average down" to a lower resolution, but merely selects a certain subset of the native resolution pixels

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