There would be less input lag at 165Hz with VSync on.
Outputting a higher FPS than a monitor refresh rate doesn't guarantee screen tear. Screen tear is caused when the monitor's VBLANK (the signal issued when it clears the screen and requests a new image) is not synced with the GPU, when this happens the monitor can grab an image before it has been fully rendered by the GPU.
With VSync on, the graphics driver waits/blocks the present command until the VBLANK signal has come from the monitor to ensure it presents a full and complete image. A side effect of this is that the game is then waiting/blocked for this command to pass before it can begin work on the next frame. (The present command is called at the end of rendering frame to flip the backbuffer to the front).
When you run higher refresh rate monitors with VSync on, the time waiting/blocking in game is reduced, as 6ms (165Hz) is shorter than 16ms (60Hz).
Hope that helps!