FreeSync does not add input delay, it's actually better than fixed refresh because it updates the image on the monitor only when the GPU produces a frame. Therefore, every frame is fully displayed as soon as it's ready.
Take for example, fixed 144hz refresh:
Frame 1 is 144hz, so full frame is displayed immediately.
Frame 2(vsync off) is 140fps, so you get half of the new frame and half of the old image on the screen at the same time (aka tearing)
Frame 2 (vsync on) is 140fps, but since it didn't make it to the monitor in time for the 144Hz refresh, it has to wait until the next refresh (input delay)
Screen tearing is noticeable, but less so at higher refresh rates. Regardless, it's still there. So by removing screen tearing, FreeSync is making frame rate drops less noticeable.