The cable you linked to allows you to connect the USB 3.0 ports on the case to a USB 2.0 header on the motherboard. It will allow the port to work, but at USB 2.0 speed instead of USB 3.0.
As for the hard drive, it should work fine. A mechanical hard drive doesn't work fast enough to actually benefit from SATA 6 Gbs. If you were using an SSD, that would be different.