It would do a very good job, but it might be a little difficult to attach it securely without damaging it. To get the white styrofoam structurally secure, you would most likely need to put 1/4" sheets of hardboard or some other reasonably strong material under it to hold it in place.
R value is 4.19 perinch thick for standard 1# foam. It is flamable though so be sure to cover it with sheetrock. I usually send 3.5 inch foam sheets to customers for use in insulating structures. But I have also sent it as thick as 24 inches. I used 3.5 in my garage walls then sheetrocked. 30 degrees without a heater when it was -10 outside.
