Again its exactly as LoL above and my post suggests.
It WILL initially cause a faster dissipation to the steel in the heatsink, but the "thermal equilibrium" will quickly be reached when the advantage of the copper would be no longer a measurable advantage. The steel and the copper would quickly reach the same temperature.
I do not believe that the copper plating would then dissipate the heat to the air much better than the steel.
So YES, an initial short benefit, but not a significant sustained one (assuming the heatsink (copper or steel) is a good thermal connection to the CPU die.
If the CPU is cycling cool-hot a lot, the copper would be better at handling the transient change times and relaying the heat quicker into the steel but thats not usually the case.
You would need a good heavy copper plate as well, why not make an all copper one to gain the small advantage?