Since you touched on the subject, let me elaborate a little, since I am also a sound engineer and a music studio owner.
Strictly speaking, deadening is a wrong word in this context, as it describes attaching something to a material to make it less prone to vibration and rattle. If we want to be correct, we should use "dampening" or "absorption". In any case, here we use a very thin material (mine is 1/4'', similar to OPs when doubled). To make sure we are effective, we should get the most of the peak of the wave to be caught within our material. Say we have a rather high frequency of 10Khz, with a wavelength of 4/3''. Our 1/4'' is 40% of the half-wave (one peak) so we can theoretically reduce it at most by that percentage if we use perfect material, but it only gets worse as we go to lower frequencies. To actually make the sound energy be converted to heat, a heavy, dense material should be used, not any light foam (with large bubbles and open cell design). The one I got seems reasonably dense with closed cell design.
Lastly, the white (pink?) noise from the road contains all frequencies, and also the very rotation of the tires and the vibrations of the suspension are certainly low frequency, but there is not much we can do about it with this solution. All we can hope for is a little bit of a reduction of the road/wind noise in the high frequencies which should be noticeable enough on itself, like removing the hissing sound from old cassette tapes, while keeping the "boominess".
P.S. Now that I am thinking about it, it is possible we also have some deadening benefit by covering that panel, as it's very possible it's resonating and thus producing its own sound, like a very crude speaker.