The reconfigurable intelligent surface (RIS) technology allows one to engineer spatial diversity in complex cellular networks. This paper provides a framework for the system-level performance assessment of RIS-assisted networks and in particular downlink coverage probability and ergodic rate. To account for the inherent randomness in the spatial deployments of base stations (BSs) and RISs, we model the placements of the RISs as point processes (PPs) conditioned on the associated BSs, which are modeled by a Poisson point process (PPP). These RIS PPs can be adapted based on the deployment strategy. We focus on modeling the RISs as a Matérn cluster process (MCP), where each RIS cluster is a finite PPP with support a disc centered on the association BS. We assume that the system uses the orthogonal frequency division multiplexing (OFDM) technique to exploit the multipath diversity provided by RISs. The coverage probability and the ergodic rate can be evaluated when RISs operate as batched powerless beamformers. The resulting analytical expressions provide a general methodology to evaluate the impact of key RIS-related parameters, such as the batch size and the density of RISs, on system-level performance. To demonstrate the framework's broad applicability, we also analyze a RIS placement variant where RISs are deployed around coverage holes. Numerical evaluations of the analytical expressions and Monte-Carlo simulations jointly validate the proposed analytical approach and provide valuable insights into the design of future RIS-assisted cellular networks.