It will be a lot noisier placed directly on the foam, but if you use a soft caulking such as DAP Alex Plus with Silicon, you will find it a lot quieter. What I can't tell you is how that compound reacts, if at all, with styrofoam.
Home Depot sells a roll of semi-clear rubbery material embeddded with cork...it is a sub-flooring with a plastic sheet base to it. I use the DAP and cut strips of this sub-flooring for my roadbed. It is cheap, I think $35 for a good sized roll that will last you six layouts.
Or, go to your carpet installers nearby and ask them if they have bits of rolls of the blue or yellow vinyl underlay, the 1/8" thick stuff. Same thing, cut the 17/16" wide strips to place directly under your ties, and fix those strips in place with an acrylic latex caulk or the DAP Alex Plus with silicone if it will not eat the surface on which you smear it. And in any case, do smear the caulk very thin. Press firmly and squirm the strips back and forth, sideways, to get the layer firmly smeared and adhered to the underside of the strips, too.