The logic behind a shiny isn't color but numbers.
The point is that, even if I have my doubts about the authenticity of this fact,
if an original Game Boy (the so called Brick) could in fact play the second generation, Gold and Silver, it wouldn't influence the possibility of a shiny's apparition, because all the data and numbers necessary to make such a thing work are in the cartridge and not in the console.
tl,dr: Yes, because logic.
Hope this helped!