Can a wild Pokémon with Run Away flee from a battle?

A friend just contacted me saying she found a shiny Eevee and she doesn't know whether to try and battle it or to just use her Master Ball, because she doesn't know if it has Run Away or if wild Pokémon can use it.

Google Fu has failed me, and I don't know what to tell her. Using a Master Ball sounds ludicrous, but if she loses the Pokémon she'll bitch at me for a week or so about it.