The equilibrium structure and thermodynamic behavior of a soft matter suspension of hard-core soft-shell (HCSS) colloids have been modeled using stochastic hard collision (SHC) dynamics [Craven et al., J. Chem. Phys. 2013, 138, 244901]. SHC dynamics includes the effects of inter-penetrability of soft particles while retaining the computational efficiency of hard collision dynamics. The HCSS colloids are characterized using two parameters: softness parameter (a measure of the propensity toward interpenetration), and core-to-shell ratio. In both, molecular dynamics and Monte-Carlo simulations, the softness parameter is seen to profoundly affect the effective packing fraction and the thermodynamic behavior of the system. Once we accounted for the trivial effects from changes in the reduced volume fraction on changing softness, we found that the inter-particle penetration continues to affect this thermodynamic behavior. The structural origin of this nontrivial effect likely lies in the loss of translational order upon increasing softness.