Thin nanoscale coating of metal electrodes by graphene promises to be a useful approach for suppressing the secondary electron yield and potential multipactor. Recent calculations showed reductions by as much as 50% for graphene over copper electrodes for energies below 125 eV, with results in good agreement with experimental data. Here, the resistance to possible degradation of this structure, in response to incoming atomic projectiles, is gauged based on molecular dynamics simulations. Our results for surface irradiation by carbon atoms (as an example) on nanoscale graphene coatings indicate a defect threshold of about 35 eV, lower surface damage for thicker layers, negligible sputtering, and defects less than 6 Å in dimension for energies up to 300 eV. The electrode structure is shown to be robust with better resistance to damage than metal alone.