On the face of it, the question in the title seems banal: NATO members' armies practice in multinational maneuvers, have certain standards to allow their armies to integrate well with each other.
So these same armies (or armed forces to be more exact) should profit from thei common NATO membership in a multilateral military force, whether it's an EU, UN mission, a "US-led coalition of the willing" or whatever constellation should be useful regardless if it's "officially" a NATO mission. Of course, I could be wrong.
My question is: Is this so? Did high ranking military personnel (of any NATO-member) ever comment on how useful a a common NATO membership is for multilateral missions outside the official NATO umbrella?