In my experience, there is no validity to the statement "everything evens out by third grade" when it is applied to a gifted child, especially one with parents who give a darn about their child's education.
At the end of K, when my wife and I first initiated talks of grade skipping, my daughter's principal voiced this statement with accompanying nods from her kindergarten teacher and school counselor. So we pulled our daughter from that (public) school and enrolled in a new (private) school. Two whole-grade accelerations later (skips of 2nd and 6th) and she's still ahead of the kids in her current grade.
As far as everything evening out, I think the gifted kids who are ahead in K, 1, or 2 will only be caught by grade 3 if they are left untaught and unmotivated.
--SF