Is it conceivably possible for a character with enhanced eyesight to shoot a rifle with iron sights as accurately as with a scope? Or are there inherent limitations getting in the way?
Not, “inherent limitations,” but you would be giving up some functionality that isn’t common on modern iron sights.
Long range marksmanship isn’t about putting the cross hairs over someone’s head and pulling the trigger. There are a lot of factors which can affect the trajectory of a bullet.
Bullet drop is the simplest example of this. As a bullet travels through the air, it is also affected by gravity, and falls towards the earth. The further you fire, the father the bullet will fall until it connects with something. Some iron sights include rangefinders, which will elevate the rear sights to account for drop.
Because the bullet is a lightweight, physical object, it is still affected by things like wind. Again, this isn’t much of an issue at short range, but at longer ranges, wind can play a significant role in where the bullet finally comes to rest. When calculating wind in long range shooting, it’s not enough to know what direction the wind is traveling where you’re positioned, but also what the wind is like at the target. In situations like this a scope can be helpful for determining what the wind is doing over there. As with drop, some iron sights are designed to be adjusted for windage. It’s not incredibly common, but these do exist.
We’ve talked, before, about how most rifle rounds are hypersonic, and that the signature crack of a rifle is, actually, a small sonic shockwave caused by the bullet breaking the sound barrier. At extreme ranges, over 2,500 yards (if I remember correctly, this value is affected by atmospheric density, which is calculated based on altitude and humidity), friction will bring the round back down through transonic speeds (around 600-700mph), at this point the shockwave will usually overtake the bullet destabilizing it and severely affecting accuracy.
When you’re talking about a sniper, the least important part of their equipment is, ironically, their rifle and scope. Those are both useful, and high quality equipment will offer the best results, but the difficult part of their job are things that have nothing to do with the hardware itself.
Beyond that, the scopes are just optics, they help a marksman hit their target, but they’re not necessary. However, the benefits they offer do go beyond simply providing a firing point.
So, the short answer is, no, your character wouldn’t need a scope, but they would still be better off with one than without. The one exception I could think of is if the have some cybernetic augmentation which provides firing solution data to the user, which is more accurate than simple optics.