I think its necessary here to point out a fact;
Sights do not shoot. Guns shoot. And good accurate ammo shoots.
If we take a bench rest rifle and lock it in a machine rest and then remove its scope and fire a 5 shot string, that string is going to be just as accurate as it would have been with the scope on the rifle.
If you can align your weapon on the same axis every time it's going to shoot up to the potential of the ammo and to the potential of it's own accuracy limitations.
Yes, it's possible to shoot MOA and less with iron sights. MANY competitive shooters have done it. Here is a pic of the very best I ever did. Now I have only shot a group with irons this small one time in my life (which is why I kept this target) but shooting at or a bit under an inch with good competitive rifles was not uncommon for me when I was in my 20s clear through my late 40s.
This was shot with a highly tuned AR-15 in 6.8 SPC at 100 meters. It measures well under 1/2" center to center. Only 4 shots however. I had a 10 shot mag and installed a new rear sight on the rifle. It took me 6 shots to touch the corner of the square. My spotter said "come up one click and left one click and shoot me a group."
That's what I did, and this is how well the rifle and ammo shot.
So to put a rest to the debate above about "dont tell me about shooting MOA"-----
Yes it's not only possible, but it's not even noteworthy in the cases of many shooters.
If the shooter has the rifle, the skill and the eyes to do it, a rifle can shoot MOA and less
without a scope. Scopes don't shoot!