Chess is an endeavor with many paths. If we take our time on our moves planning things out, then YES, I would say chess will develop our "critical thinking" for when we are away from the Board -- as we apply similar thought patterns to other tasks.
For instance when we drive a car, we anticipate future dangers by driving slower when a lot of cars on the road or weather is not ideal. However our chess and driving will suffer when games ( or driving ) are speeded up -- giving us less time to think / react -- more prone to mistakes.
No.