Yes, you can use it, but this power out don't have the switch, the power is wired from power IN to power Out.
when you power OFF the MS, on this connectore you still have the power.
Inside the power supply ATX, on the Power IN connector give also a FUSE protection, not sure if your mixer need a lot of power, BUT if will brocken the FUSE protection, you can change it.

For what you want to do, you need a Relè system switch on the midle.