Yes but even with low power modern processors you are looking at 20W load power consumption and that heat has to be taken care of.
12"*12"*6" can accomodate micro-atx so I don't think that's a fair size for mini-itx. A mini-itx board is 6.7" square so 7"*8"*4" or 7"*7"*5" or so would be an ideal size that would accomodate an 80mm fan.
20W is easily doable. This is pretty much where the Via boards these current mini-ITX cases were designed for max out. It is when you try and get above 20W that you run into problems. When your chipset alone is a constant 20W, you're fighting an uphill battle. As for fitting a ÂµATX in a 12"X12"X6" case -- good luck to you! How are you going to get the drives in there? They will have to overhang/underhang the MB, which is going to create some major restrictions in what kind of heatsinks, fans, and PCI cards you can use. Also, you will almost definitely be forced to use an external PSU. Given the limitations of what you would actually be able to do with the ÂµATX board once you got it in there, you might as well start with a mini-ITX and have a bit more room to work with for an easier installation. There is a reason there is no current ÂµATX case with both a width and a depth below 13.5". Anyway, maybe I wasn't clear. When I said 12"X12"X6" was the perfect size, I meant for a full featured desktop chipset PC using today's mainstream gear. Obviously if you are just trying to build a thin client, router, or the like, you can get by with a much smaller case. Right now, to get full features in a really tiny case you need to use expensive parts like mobile CPU and SSD drives. The idea behind 12"X12"X6" is that it would be smaller than any available ÂµATX case but still accommodate all mainstream (ie cheap) parts. My real complaint was about the height, anyway, which is always too short for any flexibility in cooling and expansion cards. 10"X10"X5" could work well enough, but I'd argue that aesthetically that is no better and just makes things overly cramped to work in.