Network densification and coordinated multi-point (CoMP) have been shown to be promising and practical approaches to meet the dramatic increase in mobile traffic demand. Motivated by the ever-increasing popularity of rate splitting multiple access (RSMA) in wireless communications, this letter proposes an RSMA-enabled user-centric remote radio heads (RRH) clustering in cloud radio access networks (C-RAN) and then develops a statistical framework to evaluate the average sum-rate and the area spectral efficiency of this mechanism under generalized fading conditions by stochastic geometry. In addition to this framework, new insights into the tradeoff between the average sum-rate and area spectral efficiency in terms of RRH clustering radius are presented. Further, two widely utilized fading models, namely Rayleigh and Nakagami-m, are discussed to characterize the fading behavior in C-RAN. Finally, simulations are demonstrated to verify the effectiveness of the proposed analytical framework.