You can’t trade Pokémon back generations (say from Gen 7 (Su/Mo) to Gen 6 (X/Y, OR/AS)), so you can’t send an Alolan-Vulpix (or anything caught in Sun/Moon) to a previous game.

If you transfer your Pokémon via ‘Bank’ from Generation 6 to Generation 7, you’ll get the form you originally caught. So a Vulpix or Sandslash…