Your mobo is 12 inches tall and 9.6 inches wide. That HIS 7850 is 9.25 inches long(6pin connector on end of card). It looks like there's more than 1 inch
between the mobo tray and the drive cage in your case. It should be fine. The 6pin connector is back under the cooler shroud a ways(out of the way).
Edit: the shorter iceQ turbo is 9.25 inches long. The iceQ is over 11.25 inches. The msi is only about 7.75 inches long. Has a better cooler too(good for OCing).