Copper has a better heat transfer than aluminium. A cool amplifier would perform better than a hot one (at least the semiconductors would live longer if nothing else).
But anyway, in my opinion that heatsink doesn't look very efficient: It is indeed pretty small and even more, it has no fins! I bet that piece of copper has also been a lot more expensive than a "less sexy", but adequate aluminium heatsink. The most stupid part is, who's going to see it when it's inside the chassis anyway! And speaking of the chassis, where are all the ventilation holes! Got to admit that the chassis looks pretty sturdy though, I bet it acts as a heatsink itself. Doesn't look that impressive IMO. Also, I wonder what "the possible sonic improvements" and "better damping" are... So far no-one has been able to prove that heatsink material, aside effects of heat transfer of course, would do anything to operation of the amplifier.