The anelastic theory of effective buoyancy has been generalized to include the effects of momentum flux convergence. Mediated by the nonlocal perturbation pressure, the dynamics tends to average over details of the forcing, yielding acceleration robust to small-scale variations of the flow. Here we demonstrate in a large-eddy simulation (LES) with a 100-m horizontal grid spacing that including the anelastic nonlocal dynamics can help capture the mean evolution of convection without fully resolving the fine-scale coherent turbulent structures embedded in the flow. Instances of convection in the LES are identified. For these, the buoyancy and dynamic contributions to the vertical momentum tendency are separately diagnosed. The diagnoses show that buoyancy is the leading effect in the vertical acceleration while strongly interacting with the vertical momentum flux convergence. In comparison, the influence of the horizontal momentum flux convergence on the vertical motion are substantially weaker. The sensitivity resulting from averaging over fine-scale features are quantified. For deep-convective cases, these contributions at the cloud scale ($\sim8$ km) exhibit a robustness—as measured in a root-mean-square sense—to horizontally smoothing out turbulent features of scales $\lesssim3$ km. As expected, such scales depend on the size of the convective element of interest, while dynamic contributions tend to be more susceptible to horizontal smoothing than does the buoyancy contribution. By verifying a key attribute of the pressure-mediated dynamics in an LES, results here lend support to simplifying the representation of moist convection under the anelastic nonlocal framework for global climate models and storm-resolving simulations.