The HD 7750 is a tiny card, if any card is capable of fitting nicely into a mini tower it would be the HD 7750. The answer is YES!
EDIT: Looking at some pics of the vostro 460, you may have to put the expansion card (whatever it is) into one of the lower free PCI slots so that the cooler of the Gigabyte OC model can fit because it does take up some width.