I take it you are referring to Emeril's recipe. He says to soak for 12 hours, not 6. Since they are not soaking in pure lime juice they should be ok. Buttermilk is also an acid and will make them VERY tender and juicy.
They certainly wouldn't "cook" as in a ceviche/seviche. Just so no one will get the wrong impression here chicken needs heat to cook (I'm sure you already know that Elf - I just don't want someone to misread this
I'd say they will be just fine. The texture should be fine since it isn't pure lime juice - I'd say that would definitely alter the texture. I made some chicken thighs one time soaked in pure lemon juice - that'll put a pucker on your face and I won't do it again!