The surrogate nuclear reaction method is being applied in many efforts to indirectly determine neutron-induced reaction cross sections on short-lived isotopes. This technique aims to extract accurate (n,γ) cross sections from measured decay properties of the compound nucleus of interest (created using a different reaction). The advantages and limitations of a method that identifies the γ -ray decay channel by detecting any high-energy ("statistical") γ ray emitted during the relaxation of the compound nucleus were investigated. Data collected using the Silicon Telescope Array for Reaction Studies and Livermore-Berkeley Array for Collaborative Experiments silicon and germanium detector arrays were used to study the decay of excited gadolinium nuclei following inelastic proton scattering. In many cases, this method of identifying the γ -ray decay channel can simplify the experimental data collection and greatly improve the detection efficiency for γ -ray cascades. The results show sensitivity to angular-momentum differences between the surrogate reaction and the desired (n,γ) reaction similar to an analysis performed using low-lying discrete transitions even when ratios of cross sections are considered.