Yes this is easily accomplished using a 5V coil rated relay powered by a USB socket. I'm left wondering how much detail you need to make this work, as there are no surprises doing it, just USB +/- to relay coil, and PS_On and PSU Gnd to the normally open relay contacts.
There are ready made widgets that can do this via software too, then you'd issue the on/off command on startup and shutdown, or jumper around the control chip to make it come on/off with USB power.
Keep in mind that your ATX PSU would always have the 5VSB live so wasting a slight bit of power when not in use. I like Larry's idea more to just use a switched mains AC power outlet and then a powered hub or whatever.