The problem with that I see is the cleat will only pinch it together in the back but split it open a bit on the top varnished side. I've had the best success in figuring out how to clamp the crack together properly and cutting the cleat to match the contour of the wood.
The best way I've found to properly clamp a crack is in the pic below. These clamps can be made from pvc pipe and are anchored with temporary cleats on either side of the crack. Alternate these with clamped cleats (as shown) and the crack should close nicely.
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