Would a cell voltage change significantly if the right-hand half-cells contained twice their volume of a solution of the same concentration? Why? What if each electrode were made from cylindrical wires instead of flat sheets?

No. A voltage reading is a result of a difference in cell potential of the cells. Even if you added the volume, it would still not affect because what matters is the concentration of the ions which give the potential gradient. All you did was add the quantity in terms of volume but the substance in it is still the same.