If you look at the map, there is no place to stage it. The border with Turkey is very small. Staging in Iraq would mean troops under attack from both sides even before they cross the border.
I don't think staging light infantry will be a problem but I don't think they'll successfully break out of the mountains, certainly not into any land that isn't already ethnically Kurd (or Baloch, but that's in the other corner of the country).