With the growing popularity of delay-sensitive applications (e.g., real-time conversational video, online gaming, and augmented reality) and future trends toward ultra-reliable low-latency communications such as the tactile Internet, performance analysis of wireless systems under the finite code blocklength constraint becomes extremely important. In this paper, we investigate the maximum achievable throughput of incremental redundancy-hybrid automatic repeat request (IR-HARQ) over the (correlated) Rayleigh fading channel under finite blocklength and delay-violation probability constraints as a function of the modulation scheme. The maximum number of HARQ rounds together with the transport block size specifies the underlying coding latency of the IR-HARQ scheme. A framework, namely the HARQ Markov model (HARQ-MM), is introduced to track the throughput and the probability of error of IR-HARQ over the Rayleigh fading channel as a function of the modulation scheme. The dispersion of parallel additive white Gaussian noise channels with finite input alphabets (e.g., pulse amplitude modulation) is analytically characterized. It is used to identify the state transition probabilities of the underlying HARQ-MM. An algorithm is developed to efficiently compute the steady-state distribution of the HARQ-MM. Extensive performance evaluation is conducted, which shows a good match between the throughput performance characterized by the theoretical framework and that achieved by the practical channel codes.