One of the promising technologies for the next generation wireless networks is the reconfigurable intelligent surfaces (RISs). This technology provides planar surfaces the capability to manipulate the reflected waves of impinging signals, which leads to a more controllable wireless environment. One potential use case of such technology is providing indirect line-of-sight (LoS) links between mobile users and base stations (BSs) which do not have direct LoS channels. Objects that act as blockages for the communication links, such as buildings or trees, can be equipped with RISs to enhance the coverage probability of the cellular network through providing extra indirect LoS-links. In this article, we use tools from stochastic geometry to study the effect of large-scale deployment of RISs on the performance of cellular networks. In particular, we model the blockages using the line Boolean model. For this setup, we study how equipping a subset of the blockages with RISs will enhance the performance of the cellular network. We first derive the ratio of the blind-spots to the total area. Next, we derive the probability that a typical mobile user associates with a BS using an RIS. Finally, we derive the probability distribution of the path-loss between the typical user and its associated BS. We draw multiple useful system-level insights from the proposed analysis. For instance, we show that deployment of RISs highly improves the coverage regions of the BSs. Furthermore, we show that to ensure that the ratio of blind-spots to the total area is below 10^{-5}, the required density of RISs increases from just 6 RISs/km2 when the density of the blockages is 300 blockage/km2 to 490 RISs/km2 when the density of the blockages is 700 blockage/km2.