We study the impact of deploying reconfigurable intelligent surfaces (RISs) in mitigating coverage gaps and enhancing transmission reliability in an industrial internet of things (IIoT) network. First, we consider a single blockage scenario and characterize the correlation between blocking events of the base station (BS)-user and the RIS-user links and study its impact on the probability of establishing a viable reflected link. Then, by considering multiple blockages, we derive the distribution of the signal to noise ratio (SNR) as a function of data size, blockage density, the number of RISs, and the deployment area. We analyze the impact of normalized blockage radius and identify the threshold beyond which the assumption of independent blockages deviates from the ground truth of correlated blocking. Finally, we compare the outage performance of this RIS-assisted system with that operated with network- controlled relays, and demonstrate that while the relays provide a higher reliability beyond a certain blockage threshold, increasing the number of RISs may help mitigate this effect. These insights offer valuable design guidelines for deploying RIS-aided IIoT networks in dense blockage environments.