Elastic diffuse neutron scattering from Cu-17 at.% Mn was measured within three planes of reciprocal space, at room temperature and at 11 K (far above and below the spin-glass temperature of 71 K) to determine the atomic and magnetic short-range order parameters. Using two samples with frozen-in states of thermal equilibrium of 483 and 553 K, respectively, the antiferromagnetic character of the spin glass was found to be robust against changes in the degree of atomic order while the ferromagnetic character is rapidly reduced with lower atomic order. This confirms conclusions of ab initio calculations by Ling et al.