My answer is no and nope. Are you saying that alone makes it an icon? I think it is a lot more complicated than you make out to be, if that is what you are saying. There's classic artistic composition, for one thing, and the "Decisive Moment" for another. Joe got it in focus, for another thing, which is no sure thing when bullets are whizzing about. There's the Moment in History that adds to it all and there's getting the photo out to a whale of a lot of people within a short time after the taking the photo. Who sees it and when makes a big difference. As I recall it was in Life Magazine which was THE place at that time for a photo to run if it is going to become an icon.
Another AP photographer got an iconic photo of an airman greeting his kids after being in a prison camp in North Korea for many years. The AP photog got the Pullet Surprise for that one and a local photo who got almost the same photo didn't get squat.
As I said, it is complicated.