It is not obvious today that NATO would welcome an Iraqi proposal, though the US and UK would be wise to support it. Turkey has long been a NATO member, so that there is a precedent.
"Not obvious?" I think we have the first candidate for understatement of the year.
And, other than the fact that Turkey has a Muslim majority, what are the other parallels? This criteria would make Iran and Yemen good candidates, too.
Just when I thought things couldn't get any weirder in the world, someone proves me wrong. I give the Iraqis three chances: slim, fat and none.