that's bullshit - any foam is an excellent heat insulator because of the trapped air.
Only closed-cell foams trap air -- this is very much an open-cell foam, a coarse one at that, and it looks like the airflow (and therefore convection and potential heat transport) through that particular foam would be pretty free-flowing.
The remaining question is whether the thin strands of copper leading from the bottom to the top will conduct well enough. Mental exercise -- imagine placing the heat sink in a super table vice and crushing it into solid copper. What would you be left with, a block of copper maybe a centimeter thick? The heat conductivity through that solid block is clearly going to be very good (A 2 inch x 1 cm cross-section block with 1 inch height works out to 0.13 K/W). But here's the kicker -- it seems like the average copper path length from bottom to top is maybe 50%-100% longer in the foam than the direct line possible in a solid block, so the thermal conductivity is only going to be 33%-50% worse. Let's say 0.26 K/W. Except it's radiating the whole way. Hardly a massive penalty for the foam factor. 100W works out to 26 degrees C over ambient in the copper alone (so yes, neglecting the actual radiation/conduction into air), which is pretty lax, but vaguely workable.
Will this foam radiate heat as well as an traditional heatsink with the same volume of copper? Probably not. But might it be an acceptable compromise of interestingness/aesthetics vs performance? Pretty shaky, probably not. But it's certainly not as intrinsically absurd or off by orders of magnitude as many here are making it out to be. If it helps, think numerically about how electrically conductive the foam would be (to clear your mind of the "omg it's foam and there's air everywhere run away" preconception), and then refer those results back to the thermal world.
Edit: Just to be clear that I basically agree that this isn't a good idea (with reservations), I offer another disadvantage: this foam would be a massive pain to clean dust from...