The stoichiometry fixes the site probabilities to gold and copper. Every site in the average crystal structure therefore has the same atomic scattering factor
(1)
The average structure factor is
(2)
At the bracket vanishes, while at it is four. Hence
(3)
The powder diffraction multiplicity is unchanged, so its coherent Bragg diffraction wave intensity equals the ordered value under the stated equal-lattice constant approximation.
The zero refers to the coherent Bragg diffraction peak of the average crystal structure. A random alloy can still give occupational diffuse scattering at the same scattering vector: the average of the squared amplitude includes fluctuations as well as the square of the average amplitude. Such background is not a surviving Bragg diffraction peak.

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