Oooh, no. And here is why: Heat. Sadly, this build won't last; I wouldn't give it six months. The non-modular Corsair "CX" units were built with some inferior Samxon capacitors that don't like heat and are known to fail early. Even without considering the radiant heat from the graphics card, you're running it at a high enough percentage of its capacity that it will cook. I also don't care for what all that [radiant] heat might do to the motherboard.
Will this HIS card fit in that case:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814161428 ? It exhausts its heat. You'd give up a chunk of performance, but 1) solve the heat problem and 2) allow for an optical drive and/or 8GB of RAM in the budget. The benchmarks show that frame rates are high enough that you're still going to get smooth 1920x1080 gaming out of it, plus you'll have something cooler and quieter that will still be running in a year or two, or three...
If the HIS won't fit, this EVGA FTW-version of the GTX660 will: http://www.newegg.com/Product/Product.aspx?Item=N82E16814130829. It costs more, but performs better than the HD7850, and still exhausts most of its heat.
Edit: I'm really happy to see m-ITX in a SBM. Without necessarily repeating it any time soon, I think a little refinement still merits discussion and maybe more testing.