The sticking of Ar on a cold Ru(001) surface covered with an Ar monolayer is studied as an example of a surface with significant static corrugation of the gas-surface interaction potential, and also substantial dynamical corrugation due to the deformability of the overlayer. Classical molecular dynamics with an empirical pairwise additive potential is used to simulate the system. The results do not fit the usual E cos(n)THETA dependence of the sticking probability on the incident energy E and angle THETA to the normal (where n = 2 is the smooth surface limit). Instead the angular dependence of sticking is a strong function of E, reflecting a changing competition between static corrugation and dynamical effects. At low energies total energy scaling (n = 0) is observed, and attributed (with the aid of a simple model) to static corrugation, a generic effect which may well apply to other adsorbate/surface systems. At higher incident energies, dynamical effects during the gas-surface collisional event are responsible for the breakdown of total energy scaling, which results in enhanced sticking for grazing relative to normal trajectories. A grazing trajectory may possess enough in-plane velocity to allow it to move away from the adatom it initially strikes before the adatom recoils from the substrate.