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It is always important to read the manufacturer's installation instructions for approved fasteners. Depending on the thickness of the foam board, the fasteners may need to be a little longer to penetrate through the studs/sheathing enough.
Hope this helps!
In a word...yes.
As Katie mentioned, you need an appropriate length fastener and a cap nail is ideal.
What you haven't mentioned is what the wall depth is as well as climate. If you have 2x6 walls, 1" foam may not be enough to keep dew point at bay.
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