Certainly. The channel roughness (Manning’s n) downstream from the dam affects the stage there. That stage is the tailwater that is used in the outflow computations for the breach. The breach computations are done using either an orifice equation (piping) or weir equation (overtopping). In either case, the outflow computation recognizes the submergence from the downstream tailwater. Result is that, for (say) higher downstream n values, the outflow will be decreased and, therefore, the reservoir will drawdown more slowly than for a less rough downstream channel. The magnitude of this effect will also depend on the geometry of the dam breach parameters and reservoir storage.