As the mobile application landscape expands, wireless networks are tasked with supporting different connection profiles, including real-time traffic and delay-sensitive communications. Among many ensuing engineering challenges is the need to better understand the fundamental limits of forward error correction in non-asymptotic regimes. This article characterizes the performance of random block codes over finite-state channels and evaluates their queueing performance under maximum-likelihood decoding. In particular, classical results from information theory are revisited in the context of channels with rare transitions, and bounds on the probabilities of decoding failure are derived for random codes. This creates an analysis framework where channel dependencies within and across codewords are preserved. Such results are subsequently integrated into a queueing problem formulation. For instance, it is shown that, for random coding on the Gilbert-Elliott channel, the performance analysis based on upper bounds on error probability provides very good estimates of system performance and optimum code parameters. Overall, this study offers new insights about the impact of channel correlation on the performance of delay-aware, point-to-point communication links. It also provides novel guidelines on how to select code rates and block lengths for real-time traffic over wireless communication infrastructures.