No, it's a different bug in the human optical system.
Impossible colors are derived from the frequency-response curve of the three standard pigments in the retina. (There are people with 2 pigments and thus have a reduced color space, and people with 4 pigments who have an increased color space.) Since the pigments are not evenly distributed, the brain synthesizes some colors from incomplete information.
The dress problem stems from luminance-color correction in the brain itself. The eye has quite an amazing dynamic contrast ratio, but a much narrower static contrast ratio. If you have picked up on clues that the photograph was over-exposed in one way, your brain interprets that as a signal that the colors are washed out. If you have picked up on clues that the photograph is undersaturated, your brain says that the colors should be brighter than the pixels are. The photograph in question gave ambiguous clues.
