You need to find out what HDMI and DP versions are supported by your display and then google their bandwidth limits.
I'd used r9 290 connected over display port to benq xl2420t and it worked fine at 120hz refreshrate, but HDMI was limited by 60hz.
Any new graphic card support 120+ hz at 1080p through dvi-d/hdmi/displayport, so it only depends on your display will it work or not.
//there is high probability that 120hz will work over DP too on your display.