If the tread width goes up equally from both sides of the center of the contact patch, then by definition the scrub radius does not change.
The problem comes when the offset is moved inwards so that a wider tire will fit inside the wheel well. In that case, the center of the contact patch also moves inwards, thereby changing the scrub radius to a higher (less negative or more positive) value, depending on the original specification.
Increasing the rolling diameter will also move the scrub radius to a higher value, since the line intersecting the king pin axis and the center of the contact patch will move to a different point.
In addition, if lowering springs are used, then things become complicated pretty quickly.
Moral of the story is that suspension geometry is complex and plays a huge role in the handling of a vehicle, and changes to this geometry need to be carefully considered for the best overall balance.
Simply put, it is best to keep to the original rolling diameter within a 3% to 5% window and thus geometry as much as is possible.
