Free floating a barrel is not just about correcting/helping shooter error. It does make the rifle itself capable of better accuracy. It has to do with how the barrel vibrates from shot to shot. Even if you assume there is no human error, in general, a free floated barrel will still be more accurate than a non free floated barrel. Thats why nearly every precision rifle has a floating barrel, iron sights or not. Whether you will notice the change in accuracy depends on the rifle and how you are shooting it.
ETA: I am not talking about shift or "combat accuracy". This is about free floating and accuracy in general for the OP.