Input lag will be decreased by up to 1 frame of what the monitor can display.

Say you have a 60hz monitor and try to render at 120fps, the completed images are sent 0.5 frames earlier(counting with 60fps as a base). You try to render at 300fps, the images arrive at 1/5th of the original 60's 1, so you win the remaining 0.8 frames.

As you can guess, this is most of the time not worth it though, as in that last example the GPU still does 5 times the work just for a marginal increase.

If you have a monitor that has Freesync/Gsync, the ready frames get sent immediately, so no need to render above the monitor's refresh rate.