This study deals with the computational analysis of the kinetic processes of microbial electrolysis cell-assisted anaerobic digestion (MEC-AD) for treating raw-waste-activated sludge (WAS), compared to conventional AD, as well as investigating the effect of the organic loading rate (OLR) on the system’s performance. The aim was to derive a mathematical model for the study of MEC-AD using the ADM1 framework, which can be utilized to extract the effect of an applied potential on the kinetics of AD. The experimental data were obtained from the operation of two identical reactors (an AD reactor and an MEC-AD reactor), which were operated at different OLRs. The kinetic parameters extracted from the ADM1 showed that the MEC-AD reactor yielded improved biomass yields, substrate consumption, and first-order disintegration rates, with a predominant contribution to the disintegration of complex particulates, which increased fourfold compared to the AD reactor. Moreover, it enabled operation at higher OLRs (achieving the highest divergence from the AD reactor at the OLR of 4.14 gCOD/(L × d)), therefore accelerating WAS treatment, as well as showing an improved performance at increased solids retention time (SRT). The ADM1 exhibited efficient adaptability and predictability of the kinetic processes and can be effectively used for the optimization of the MEC-AD operation.