If carpenter ants can chew through wood, Styrofoam is not a problem to them.
I have found them in Styrofoam on a number of occasions. Structures with Stucco have lots of issues with Carpenter Ants. Hot tubs, roofing material, interior wall insulation, exterior wall insulation are a few of the places that I have found them.
The particular images of Styrofoam is from basement wall insulation.