Do you think CG placement affects the high speed turning radius of a plane?

I'm talking RC Combat here, where we run full throttle, full elevator, and get as close to snapping out of turns as possible. So, low speed isn't an issue, we're talking max-G loading turns here.

I know that CG location makes a huge differnece with how much elevator throw you can (or have to) use to snap out of the turn, but does the turning radius actually get smaller with a more aft CG?

My experience seems to indicate that if the CG is too far forward, you can't pull the nose though, but if it's too far back, you snap out earlier, so you need to be in a fairly small range. It also seems to vary a lot with the airfoil, some airfoils seem to be much more "picky" about the CG location in a turn than others.

However, part of me thinks that my "expereince" is really off a bit, and what I'm really noticeing is the interaction between the elevator throw and the CG, not the CG by itself. That if the elevator throw was properly adjusted for any given CG, that the resulting turning radius would be exactly the same. (A rearwards CG will be quicker at getting in to and out of the turn, while a more forward CG will take a while to change AOA from level flight to just below critical AOA).

I say this because given a set weight and airspeed, turning radius should be determined only by the critical alpha of the wing, right? At critical alpha, you're produceing as much lift as the wing can possibly generate (and lots of drag too), which means you're turning as tight as you can. increase alpha beyond that and you stall. I don't see how CG would affect the critical alpha or the lift generated at that AOA? Am I missing something?