In this work, we extend the use of GCNNs to predicting the formation energy and bulk modulus as a prototypical elastic property of solid solution alloys for disordered atomic configurations in different types of optimized crystal structures with fully relaxed volumes that span the possible compositional range of the binary alloy. As an illustration, we train the GCNN model on an open-source dataset for the nickel-niobium (Ni-Nb) alloy that provides formation energy and bulk modulus calculated with the embedded atom model (EAM) empirical potential for several atomic configurations with optimized crystal structures. We investigate the performance of the GCNN with respect to the radius cutoff, which determines the size and thereby the computer time and memory requirements of the surrogate model, as well as two different graph convolutional layers that are implemented in the Pytorch-Geometric open-source library, namely CGConv and PNAConv, and report the mean absolute errors (MAEs) for combinations of cut-off radius and GCNN type. Our numerical results show that the GCNN model is able to learn the dependency of formation energy and the bulk modulus with respect to the crystal structure over the possible compositional range, but the prediction of bulk modulus is affected by greater deviations from ground truth data than energy predictions.