You could test for yourself if you have a multimeter, ohmmeter, or continuity tester, but I believe that there is already a direct connection between the case of the PC and the ground wires in the power supply plugs. And I believe there's also a direct connection between the ground wire of a USB jack and the ground wires in the rest of the PC, but there is no reason I can think of that a USB port would have to be designed that way so you'd better check for yourself on your particular computer.
If you test it with an ohmmeter and it reads "0 ohms" or if you use a continuity tester and it gives a continuous beep, then there's already a wire present so adding another one is fine.