>>31540304No.
Shininess in G1->G7 is based on DVs (the IV equivalent).
A pokemon is shiny post-transfer if it has 10 ATK DVs, 10 SPC DVs, 10 SPE DVs, and 2,3,6,7,10,11,14,15 DEF DVs.
The legit mew has perfect 15/15/15/15 DVs.
It can thus never be shiny.