As capacitors have negative and positive charges seperated by a thin layer, you would get a strong compression force across the layer. There would also be fairly large repulsive forces acting along both surfaces of the insulating layer. The lateral repulsive force would be partially countered by the lateral component of attraction from the charges on the opposite side of the layer.
With one or both surfaces covered in carbon nano tubes, there would also be a repulsive force along the surface of the tubes, tending to make them stretch in length and in diameter. However each tube would also be attracted towards the layer by the opposite charges on the other side. The carbon nano-tubes would thicken the layer of charge on either side of the insulating material.
I suspect that voltage at which the insulating layer starts leaking is much lower than the voltage at which it tears apart.
