I suggest running a test. If you can obtain/purchase some carpet squares, ones you can return if you don't use, set up a run of track with and without the carpet squares underneath. See if that makes any difference to you. You do not have to cut the squares for the test, your just trying to determine if there's a difference in sound/noise.
Beyond that, try cutting a square to fit under your track as you envision. For example, the width of the track plus a little more. This might tell you how much effort is involved and may change your overall work calculus a bit.