No sight on a rifle effects its accuracy. Fired when held in a machine rest withouit sights, a rifle still shoots bullets into some sort of group. All the sight does is help one get the groups centers at the point of aim.
Of course, if the scope doesn't always keep its adjustable optical axis the same direction and amount relative to the bore axis, then that degrades the rifle-ammo accuracy that one will see using the scope to aim it.
You can learn where the non-range focusing scope's parallax free at by mounting the scope in a fixed position then looking through it with a small monocular or even one side of a pair of binoculars. Move that around looking through the eyepiece at some distant target and whatever range the target doesn't move relative to the reticule is the range it's focused at. Doing this will also check an adjustable scope's range markings are accurate. Some are way off. A Nightforce scope I checked out some years ago focused at 150 yards when its objective lens barrel was set to infinity.
US Navy Distinguished Marksman Badge 153
Former USA Palma Team Member
NRA High Power Long Range High Master
NRA Smallbore Prone Master