Will the Asus VG248QE work at 144hz with this build – http://pcpartpicker.com/p/jqrfFT?
Monitors should work on any (working) computer as long as you can connect them together.
But yes, the VG248QE should work just fine with your configuration. Just be aware that if you are using an HDMI cable to connect it you won't get more than 60Hz. So better stick with the supplied DVI cable or use DisplayPort.