Copper from sulfate baths without and with added inorganic pigment particles based on strontium aluminate doped with europium and dysprosium (SrAl2O4: Eu2+, Dy3+) was electrodeposited on a brass cathode by a galvanostatic regime. Morphological, structural, and roughness analysis of the pigment particles, the pure (pigment-free) Cu coating, and the Cu coatings with incorporated pigment particles were performed using SEM, XRD, and AFM techniques, respectively. Hardness and creep resistance were considered for the examination of the mechanical properties of the Cu coatings, applying Chicot–Lesage (for hardness) and Sargent–Ashby (for creep resistance) mathematical models. The wettability of the Cu coatings was examined by the static sessile drop method by a measurement of the water contact angle. The incorporation of pigment particles in the Cu deposits did not significantly affect the morphology or texture of the coatings, while the roughness of the deposits rose with the rise in pigment particle concentrations. The hardness of the Cu coatings also increased with the increasing concentration of pigments and was greater than that obtained for the pigment-free Cu coating. The presence of the pigments caused a change in the wettability of the Cu coatings from hydrophilic (for the pigment-free Cu coating) to hydrophobic (for Cu coatings with incorporated particles) surface areas.