I doubt it will fit, but with some case modifications like cutting off a portion of the top left corner it will definitely fit. http://www.youtube.com/watch?v=nMhsah88_TI
^ The case with a HD 4670 (7.5" in length). Add another 5.5" and it may not fit.
I recommend just calling the manufacturer and asking for the length allowed for graphics cards on the case.