Oxide-supported Cu nanoparticles and clusters catalyze a variety of important reactions, such as CO/CO2 hydrogenation to methanol. Recent studies demonstrate that also sub-nanometer clusters consisting of only a few atoms can actively catalyze chemical reactions. In this study, we investigate the interaction between Cu4 clusters and silica-surfaces, considering the de-hydroxylated and the fully hydroxylated α-quartz surfaces. We also considered various dopants such as Ti- and Nb-ions substitutional to Si, respectively, in order to see if an electronic change of the support has an effect on the reaction of the supported cluster. We find that hydroxyl groups can enhance the adsorption energy of the cluster, whereas the dopants have only little effects on the adsorption mode of the Cu cluster. On the fully hydroxylated surface, the cluster may react with the hydroxyl groups via reverse hydrogen spillover. Finally, we explore the reactivity of the silica-supported Cu4 cluster in terms of acetylene trimerization, for which extended Cu surfaces have shown catalytic activity. We find that this reaction should occur with activation barriers below 0.8 eV; Nb-doping of the support does not seem to produce any direct effect on the reactivity of the Cu tetramer.