Imo I don't see why you couldn't play a fey. Just would make a couple really basic changes.
1st: Your High Concept must be what type of "monster" you are.
2nd: Compels based on your High Concept become mandatory, they cannot be ignored.
3rd: You receive no fate points from a compel of your High Concept.
That fixes the free will vs. nature debate, as your character no longer has free will.
Doubt any GMs would saying no to that (unless they are fairly lazy and don't want to do deal with it) as you just gave handed them the keys to your character's soul (if it has one).
Now the effects of this might be very messy, and well depending on what happens and it is very likely that the character could be turned against the party. *Shrug* that's the nature of the beast though. Could make for some really good and humorous situations though. The fact that all bargins MUST be kept and the character MUST always tell the truth... hmmm so much fun. Regardless I would definately would want to run it by all the other players before brought it to the table.
Also makes me wonder if that saying from Peter Pan has any truth to it in the DV ("Everytime say you dont believe in fairies, a fairy dies").