Every PC will support 144 Hz.
The thing however, unless you are able to push that many frames, you will not actually see them.
60 Hz monitors display up to 60 frames. Meaning if you are getting 100 fps, you are only seeing 60.
therefore, 144 hz display up to 144 frames. Meaning you will see all 100 fps you are getting, but only those 100 and not more.
Thus unless you are gaming at 720p, i do not think that your 580 will be pushing enough frames in those games to actually make a difference for you.