It should have no problem staying in place but it needs to be covered with a thermal barrier like drywall. Only rigid foam rated to remain exposed if Dow Thermax with a heavy foil covering. But finding it is difficult and a bit more expensive. The orange box web site shows they have it, but in my area only the 1" can be ordered in any reasonable quantity. You could install 1" pink or blue and then cover with 1" of Thermax.
Now, why 2" of foam? What is your climate zone and required amount of basement insulation. The reality is, above grade plus a foot or two is the high loss area. Below that the ground doesn't get that cold and any heat lost there has to travel through several feet of soil to finally escape. Essentially the soil acts as added insulation.
I don't want to talk you out of the 2", but the most important area is the rim joist, air sealing, and the exposed concrete. I like a couple of feet below grade as well, but this would take care of 90% of the heat loss.
+1 for screwing into concrete, concrete walls are often inequal and would need a lot of glue to fill the gaps
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