I do not recommend using rigid foam instead of plywood/Homasote. I was only recommending the OP use it in place of Styrofoam because it will hold the nails better to keep his Atlas or GarGraves track in place.
I used 1" thick rigid foam on a 12"x12" grid of 1x3s with RealTrax on a temporary layout a couple of years ago and it was noisy. To be sure, RealTrax is noisy to begin with, but the foam seemed to resonate the noise both above and below the layout. I used it for weight because I had to move my 8x10 layout (2 sections) to the garage for 1 holiday seasons (Easter and Thanksgiving/Christmas) so we could use the dining room. It might have been less noisy with a layer of 1/4" plywood or something between it and the grid, but I never took the time to test that. By then I had decided I was not going to use foam a sa substitute for Homasote or some other sound-deadening material.
Because my grid was 12x12, I had no problems leaving my 4-6-0 steamer and 5 passenger cars and buildings sit in place for most of 2 years. However, I don't know how it would be if a track ran parallel to the cross-member and all the weight was on a 16" wide section of 1" foam. I'm sure 2" foam would work though, but most (all?) layouts I've seen using foam also had a layer of plywood and the foam only substituted for the layer of Homasote. This was done so they could more easily cut rivers and valleys, but it seems like a waste to me to top an entire layout with 2"-4" of foam just to cut a river. IMHO, there are better ways to do that, such as lowering that section of the bench work.
Similarly, it seems like a waste to cover an entire layout with Homasote, but that's often easier and certainly less messy. I don't know though if doing so reduces the overall noise compared to just laying the Homasote under the tracks. If you do that, you can add a layer of 1/2" foam to make things even across the layout, then use 1"-2" foam to build up mountains, etc. Since my "L" layout is small at 4x8x10, I intend to just cover the whole layout. I think I'm going to eventually need 5 sheets whether or not I use full sheets and I really don't want to deal with piecemeal cutting, etc.