So... wait. You've got Buffy characters going on a trainer's journey, but there's no Pokémon?
Do you mean you just want them to go on a journey, or do you mean this isn't Mystery Dungeon? Because the latter one ("this isn't Mystery Dungeon") is kosher and called a crossover -- albeit a crack one because the two fandoms aren't entirely compatible. The former one (the one where they're on a journey and they literally have no Pokémon) just means you're taking Pokémon town names but not keeping anything else, at which point, you're better off sending them off on a quest within their own universe (considering how much about the Pokémon world relies on... well, Pokémon).
In other words, first off, what made Buffy awesome is the fact that she fought demons and other occult stuff. That was pretty much the point of the series and the point of her existence by the end of it. I'm having difficulty imagining Buffy becoming a trainer and not fighting off the occult but still being who she is. Same thing with the others, especially Willow (considering how ingrained she is in the magic world). Still, it's a crossover, so it might work if you put some thought into it.
But even more than that, I'm very curious about the "no Pokémon, just them as trainers" statement because it's a bit vague.