This is a half answer, because I don't know enough about Pokemon Amie yet. However, I didn't really think this is a comment so...
It would evolve into a Leafeon/ Glaceon. I tried it with my Eevee in Platinum, and it evolved into Leafeon near a Mossy Rock despite having the happiness for Espeon/ Umbreon.
Mossy/ Icy Rock overrides the happiness quota.
On this basis. I suspect that Mossy/ Icy Rock will override the Pokemon Amie quota as well, because you have to seek them out. Moreover, there is only one place in the game to evolve Leafeon and Glaceon respectively, whereas you can evolve Espeon/ Umbreon/ Sylveon anywhere.