On the MkIII, the Cu-180 mat isn't a problem. It's a bit iffy on the MkII, however. It's not about the total mass of the platter but rather its moment of inertia. The amount of correction the MkII servo system makes in case of speed variance is related to a fixed value for moment of inertia. The total moment of inertia with the Cu-180 added is almost twice the stock value, so speed correction will be inaccurate, though possibly not audible.
John
John