Cluster-randomized trials (CRTs) of infectious disease preventions often yield correlated, interval-censored data: cluster randomization induces dependence between observations from the same cluster, and event occurrence may be assessed only at intermittent clinic visits. This data structure must be accounted for when conducting interim monitoring and futility assessment for CRTs. To that end, we propose a simulation-based approach to conditional power estimation when outcomes are both correlated and interval-censored. We use available interim data to non-parametrically estimate the survival distributions in the intervention and control clusters, and then project these survival curves through the end of the study based on assumed changes to the baseline hazard and hazard ratio. We repeatedly generate correlated, interval-censored observations from these full trial curves and use these simulated end-of-trial datasets to assess the conditional power. Simulation studies demonstrate that our proposed method provides reasonable conditional power estimates across an array of intervention effects and degrees of clustering.