Nope, black holes have entropy proportional to the surface area of their event horizon. So the more stuff they engulf, the more their entropy increases, and thus they satisfy the 2nd law of thermodynamics just like everything else.
Has this been observed, or is it more: here's some math that makes entropy even possible because the alternatives sound unlikely? I'm betting on the weird, things like the universe being generative on a macro scale and entropic in local timespace, wherein dark matter is merely newly created matter not in another universe, but in this universe, maybe some unknown interactions between the unstoppable force of expansion and the immovable object of a black hole's gravity. I'm probably blathering, I'm not a physicist.
It's a very interesting and active area of physics actually: https://en.wikipedia.org/wiki/Black_hole_thermodynamics