Will these PC parts work together?

Yes, they will work really well.
GeForce GTX 680 has a max TDP of 195W and -requires 38A and a 550W PSU minimum.However i recommend you a better branded certified 600W PSU from Seasonic,XFX,Corsair(TX,HX,AX series), Antec.
you will get something near to this:
http://www.google.com.cu/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CCsQtwIwAA&url=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D6KcemJKiI0w&ei=FSzAUtjIK5KCyAGKnIGoDA&usg=AFQjCNGkrA4JiYcx7qtTcaWlYXxy-tubWQ&bvm=bv.58187178,d.aWc
Some BF4 Settings and/or Performance Tips:
http://forums.guru3d.com/showthread.php?t=382075