Experiment: same image, make a gamma-corrected and a linear version. Filter>Blur>Pixelize the whole image. The two images produce the same color (make a screenshot with the two images side by side, import into Gimp, explore with Pointer dialog), yet the average of the gamma-corrected value is unlikely to be the same as the one of the linear values. It appears that Gimp does the average of the gamma-corrected values whether the image is linear or gamma-corrected, because this is how our eyes see it.
If you use the pointer dialog, you'll notice that the RGB(%) display and the "pixel" display aren't the same in a linear image but are identical in a gamma corrected image.
If you use the pointer dialog, you'll notice that the RGB(%) display and the "pixel" display aren't the same in a linear image but are identical in a gamma corrected image.