A:Answer Depends on the game and the resolution you're using.
Most games do not cap the framerate.
Now, you won't be able to run graphics-heavy games at 1440p. with resolution around 165 with a 1060, but likely can if you bump the resolution down to 1080p (I highly recommend maximizing frame rate over resolution for game performance for smooth gameplay).
This is a terrific monitor especially for when you upgrade that 1060 but won't be spending $800+ for a GTX 3080 or better.
1440 at 165Hz, sitting a couple of feet away, is a world-class experience for anything less than spending extravagantly for a gaming setup.