First one would have to control the rotation.
The laws for turn rate are not a law of nature, I would be hesitant to conclude something is not possible based on that law. Rather they provide a way of estimating the design envelope for current kite designs.
For a kite i believe its simple, just integrate «L/D» over the wing. The difference in left and right should state the natural radius of flight for a wing.
Furthermore, kite networks complicate this, tethered wings will turn at any radius. The fit of natural radius and forced radius will show itself in roll control. The cross influence yaw-to-roll becomes more important for smaller loops.
I would also state that for rigid wings with tail, turning rate works differently than a kite providing some drag at either tip.
The maths is there for anyone who cares to go into the details. Many things are possible. Turning rate is of course affected by AR and wingspan, but there is so much more to it that one should not draw conclusions.
One conclusion we could draw, is that for a single wing on a tether, in order to loop (in smaller radiuses with high speed), it must have the sum force pointed somewhat towards the center of rotation. This is a cosine loss of sorts, and cant be avoided.