Distance from target plays an important role here, as well as shooter's experience.
Quick answer to your question, you may have more room for the fudge factor if you use sights, than relying on good hand-eye coordination.
(Long dribble part below)
This is all subjective, and I'm sure someone else could chime in better here but from my experience at 12-20 feet you can deliver really good (and quick) shots center mass just by getting what they call a flash sight picture. Basically, your vision is focused on your target and as the gun comes up to full extension into your line of sight, you get a brief superimposed view of your front sight. As long as the front sight is "somewhere" in the rear sight notch, and you press the trigger straight to the rear you should get combat accurate hits. Where it gets dicey (at least for me) is after 20 feet, I will make more of an effort to align my sights, of course YMMV. From arms distance to 10 feet I honestly dont even use sights, I rely on my muscle memory and natural point of aim. :icon_neutral:
I read somewhere in one of Mas Ayoob's books that instinctually a human will focus on a threat in front of them and get a bit of da ole' tunnel vision.
As with always, if you would like to try working with a flash sight picture, practice slowly and gradually begin building speed. Doing everything consistently is the key: Consistent grip, draw, placement of support hand, extension, acquirement of front sight, touch and press trigger. After lots of practice and a couple thousand rounds (not kidding), you begin to notice things like you begin to acquire your front sight a lot sooner, as it comes into you peripheral vision and as the round goes off, you find yourself "tracking" your front sight through the recoil until it comes back to rest (center of mass hopefully) ready for the next press of the trigger.
Good luck