NATO was set up to stop the Soviet Union from enslaving the remaining free half of Europe. Or rather to "keep the Russians out, the Americans in and the Germans down." Peak oil is not an energy crisis. It is a liquid fuel crisis.
If you look at Iraq which is indeed under occupation there are troops there from NATO nations, like the UK, the US and Poland (at least there used to be Poles, I'm not sure if they're still there). But there are also major NATO nations, like Germany who haven't deployed troops there while there are troops there from non-NATO nations. Remember the third(!) largest contingent was from the non-NATO nation of Georgia.
So it's really hard to find a correlation between NATO membership and deployment of troops in foreign nations. NATO nations and non-NATO nations alike do it. Peak oil is not an energy crisis. It is a liquid fuel crisis.