Yep! And here's why:
In Generation II, shininess was determined by IVs. You needed Speed, Defense, and Special IVs of 10, and an Attack IV of 2, 3, 6, 7, 10, 11, 14 or 15. If you have those IVs, they are shiny (source)
If you transfer over a Generation I Pokemon with those certain IVs, the Pokemon will appear shiny.
This is proven in this footnote in Bulbapedia about Mew Machine Mews:
Mew distributed to Generation II games cannot be Shiny. All Mew distributed to Generation I games have a fixed set of IVs which do not match the requirements to be Shiny.
This means that if the Mew had matching IVs, all Mews that came from Mew Machines would be shiny!
So,yes, it is possible.