Yes it would. Adding material generally makes thermal conductivity worse. There is no material with negative thermal resistance, so adding more will always increase thermal resistance by at least a bit.
The only exception is 3D geometries, where an increase in surface area due to the extra material can outweigh the effect of the added material, and lead to a net increase in thermal transfer.
This can lead to a paradoxical effect, where ADDING insulation around a pipe leads to HIGHER transfer than with less insulation material, because the added material increases the exterior diameter, and therefore surface area.
(Heatsinks are also a good example. It is more material than just the component by itself, but increases surface area by such a massive amount that it more than outweighs the added material)
In this case it isn’t about improving heat transfer through the bottom of the pan, it’s about improving heat transfer across the bottom of the pan.
The heat will travel through the pan more slowly because of the added material, but due to coppers extremely high heat conductivity, the copper base will heat very evenly, even if the heat source is unevenly applied, and therefore evenly transfer that heat through the steel layer.