Well, to actually answer all your questions ;-)
The benchmarks for the 970, ultra preset @ 1080p on a 144hz monitor all say no, you won't hit that refresh rate/fps. Certainly not for those games. I can say that because @ 1080p, on 60hz monitors the benchmarks for any of those games don't reach over 100 on ultra. Older games will be hit and miss.
That said, you will notice (or feel) a big difference over the 480 and 1050p (sic?)
If you're serious about gaming with that refresh rate you may want to consider getting a monitor with gsync. It will help. Also, if you're serious about gaining an edge over opponents, reducing the quality will get you that framerate and smoothness that you need.