The effects of annealed site dilution on the nonequilibrium ordering process in the two-dimensional Ising model with a nonconserved order parameter have been studied using Monte Carlo simulation. It is found that the transient development of a local order that is larger than the equilibrium order (overshooting), as recently reported in the pure Ising model [H. Gilho/j, C. Jeppesen, and O. G. Mouritsen, Phys. Rev. Lett. 75, 3305 (1995)], persists in the dilute model and is accompanied by a depletion of the vacancies within the ordered domains.