Use an aluminum case as a passive radiator?

I've read about how an aluminum case doesn't really help with cooling unless the CPU was to come in direct contact with the case. I was thinking: What if I used a water block that was fairly large, such as one for a hard drive, and placed it in contact with the side of the case. Wouldn't the case then become in effect a heatsink for the water cooling system? Even better might be to have some metal tubing welded to the side of the case that zig-zags to cover the entire side, in effect a passive radiator, without any visual external indication of modification. It just seems like a waste to not make use of all that aluminum. I'm curious what people's thoughts are on this.

The case doesn't have a great amount of surface area, relative to a radiator. It also doesn't move the heat around as well as a radiator, and it's very probably painted. All that means that it's a poor radiator, but it has a SLIM chance of working.

A very slim chance of working. The extra surface area is surprisingly minimal, and trying to find a waterblock large enough to contact the case...just wouldn't work. You could possibly try zigzagging tubes over the case, but that would be a lot of work. Easier to get another radiator or something, IMO.

Well, my case is anodized, not painted, and both sides are removable. It's also a full tower case, so the side is pretty big. I realize that since it doesn't have fins it still doesn't have the surface area of an actual radiator, but I was primarily thinking of it as supplemental cooling anyway