In the past, you can get items to go to special areas where pokemon live. For example, the flower paradise was an event place. You could get shaymin in flower paradise and there is a rare chance of it being shiny.
However, the pokemon that are given out as event pokemon (the ones you have to pickup from the man in the pokemart) are always programmed to be shiny or not. It is not possible to get a shiny pokemon this way unless it specifically said so, like the shiny beasts.
If we got a mew event, it would either be an item to go to an area with mew on it, or one that we get right from the pokemart. If it's the former, the mew may be shiny. If it's the latter (which is probably more likely), it won't be shiny.