Gold-coated iron oxide core-shell nanoparticles (IO-Au NPs) are of interest for use in numerous biomedical applications because of their unique combined magnetic-plasmonic properties. Although the effects of the core-dielectric constant on the localized surface plasmon resonance (LSPR) peak position of Au-shell particles have been previously investigated, the impact that light-absorbing core materials with complex dielectric functions have on the LSPR peak is not well established. In this study, we use extended Mie theory for multilayer particles to examine the individual effects of the real and imaginary components of core refractive indices on Au-shell NP plasmonic peaks. We find that the imaginary component dampens the intensity of the cavity plasmon and results in a decrease of surface plasmon coupling. For core materials with large imaginary refractive indices, the coupled mode LSPR peak disappears, and only the anticoupled mode remains. Our findings show that the addition of a nonabsorbing polymer layer to the core surface decreases the dampening of the cavity plasmon and increases LSPR spectral intensity. Additionally, we address apparent discrepancies in the literature regarding the effects of Au-shell thickness on LSPR peak shifts.