GTX 1070 with a 144hz 1080p monitor

Currently running a 1440p60hz monitor and a GTX 970. I want to move onto 144hz but my concern is that I am not going for Freesync or Gsync, to keep costs down. Maybe one day, but the 1070 is eating up my budget. I've watched some YouTube videos on the tech, but I'm wondering if it'll be a waste just getting a 144Hz monitor.

I've been told that a rx480 won't take advantage of the 144hz, but not too sure. I play overwatch, WoW, For Honor, BF1 and other old titles.

Thanks.