The nonstructural protein 12, known as RNA-dependent RNA polymerase (RdRp), is essential for both replication and repair of the viral genome. The RdRp of SARS-CoV-2 has been used as a promising candidate for drug development since the inception of the COVID-19 spread. In this work, we performed an in silico investigation on the insertion of the naturally modified pyrimidine nucleobase ddhCTP into the SARS-CoV-2 RdRp active site, in a comparative analysis with the natural one (CTP). The modification in ddhCTP involves the removal of the 3′-hydroxyl group that prevents the addition of subsequent nucleotides into the nascent strand, acting as an RNA chain terminator inhibitor. Quantum mechanical investigations helped to shed light on the mechanistic source of RdRp activity on the selected nucleobases, and comprehensive all-atom simulations provided insights about the structural rearrangements occurring in the active-site region when inorganic pyrophosphate (PPi) is formed. Subsequently, the intricate pathways for the release of PPi, the catalytic product of RdRp, were investigated using Umbrella Sampling simulations. The results are in line with the available experimental data and contribute to a more comprehensive point of view on such an important viral enzyme.