Dissociation of HCl embedded in dimethyl sulfoxide (DMSO) clusters was investigated by projecting the solvent electric field along the HCl bond using B3LYP-D3/6-31+G(d) and MP2/6-31+G(d,p) levels of theory. A large number of distinct structures (about 1500) consisting of up to five DMSO molecules were considered in the present work for statistical reliability. The B3LYP-D3 calculations reveal that the dissociation of HCl embedded in DMSO clusters requires a critical electric field of 138 MV cm-1 along the H-Cl bond. However, a large number of exceptions wherein the electric field values much higher than the critical electric field of 138 MV cm-1 did not result in dissociation of HCl were observed, in addition to several cases wherein the HCl dissociates with an electric field less than the critical electric field. On the other hand, the MP2 level calculations reveal that the critical electric field for HCl dissociation is about 181 MV cm-1 with almost no exceptions. A comparison of calculations carried out using the MP2 and the B3LYP-D3 levels suggests that the dissociation of HCl embedded in DMSO clusters is bistable at the B3LYP-D3 level, which is an artifact, suggesting that care must be exercised in interpreting the processes of proton transfer. The answer to the question raised as the title of this paper is NO.