The model analyzed in this work, in reference to the actual experimental studies of VSC, is perhaps too simplistic -one system mode, one cavity mode, one molecule, and no solvent-induced dissipation or cavity photon losses. A single system mode means that there is no IVR within the system and hence the influence of the cavity in terms of altered IVR pathways and the consequence for the isomerization reaction cannot be ascertained. We note here that cavity-system resonances can survive under weak dissipation limit (frequency mismatch or detuning smaller compared to the mode lifetimes) and may be especially robust due to the harmonic nature of the cavity mode. In a recent study , related to the De Leon and Berne model , Wiggins have shown that under suitable conditions the classical dynamical features that control the reactive flux can persist in the presence of a bath. More pertinent is the issue of the collective regime. An important question in this regard that remains to be answered, and crucial for explaining mode-specific effects in the VSC experiments, is whether the chaos-order-chaos transition will survive in the many body limit. Nevertheless, even for this "zeroth-order" model our study illustrates the complexity of the cavity-system dynamics upon varying the photon frequency.