>It is also possible for Wally to catch a Shiny Ralts in the tutorial. However, it will not stay Shiny in subsequent battles.
NPC's (Non-Player Characters) are programmed not to have Shiny Pokémon so again the answer is no.
This is the same case as if there was a Shiny Starter Pokémon at the beginning of the game and you picked the Starter that's type was weak to that of the Shiny Starter Pokémon, resulting in your Rival choosing the Shiny Starter Pokémon. When your Rival challenges you to a battle he/she will send out an Ordinary Pokémon.
So for example if there was a Shiny Bulbasaur and you choose Squirtle instead, causing your Rival to choose the Shiny Bulbasaur, when he challenges you to a battle he will send out an Ordinary Bulbasaur despite the Bulbasaur he just choose being Shiny.
Sources: 1 | 2