Vision-language-action (VLA) models offer a promising path toward general-purpose robot manipulation. While inference latency can affect task success in a constantly evolving physical world, the relationship between latency and task success rate remains poorly understood. In this paper, we introduce VLALagBench, a comprehensive benchmark for studying VLA inference latency sensitivity across task types, object speeds, execution modes (synchronous and asynchronous), and VLA policies. Using VLALagBench, we find that even a modest inference latency of 100 ms can nearly halve task success on moving targets, with sensitivity varying substantially across tasks and policies. These differences reflect task-specific requirements for precision and continuous motion. By overlapping inference with action execution, asynchronous execution can recover some of the lost success at the cost of more frequent inference requests. Building on these findings, we develop an empirical model that predicts task success from limited calibration data, achieving root-mean-square prediction errors of only 5.7-7.8% across various VLA policies. Given an inference system's latency and per-robot throughput, these predictions guide the selection of system-specific VLA algorithm configurations to maximize task success. We believe VLALagBench and these findings provide a solid foundation for future robotics algorithm-system co-design.