Actually screws can effect the sound .....I screwed a horn speaker cabinet together ..then glued it only  the difference was not subtle. this may have had nothing to do with the distortions of magnetic fields and more to do with a more rigid construction. But the spound was far more open and natural after screw removal.

As an aside if you place an object in a magnetic field it will distort the field.....so I have no doubt that steel screws will play old harry in the same way.