If I brine a Turkey for only three hours and then let it air dry in the fridge for at least 12 hours will the flavor of the brine be affected?

That's a short brine, but you're smart to let it dry out. If I had a choice between brined turkey or turkey allowed to dry, I'd choose dry. The crispy skin is the best part. Also, you will get more of a turkey flavor with the brine that short.