Yes.
Basic accuracy of a firearm has nothing to do with the type of sights. Basic accuracy is built into the firearm. Remove the human factors; eyesight, sight picture, repeatability of hold and how it affects recoil etc, and the firearm will tell you how accurate it is. That's why Ransom Rests were invented for pistols, to remove the human factor. All adjustable sights add is being able to move the point of impact to the point of aim. They do not increase the inherent accuracy of the firearm. Adjustable sights may also be easier to see than some of the old fixed sights. But someone who is used to fixed sights, and knows how to allow for any adjustments needed by holding off to one side or holding up or down, will be able to achieve accuracy just as good as someone with modern adjustable sights.