Does the thickness of the tread change the total rise?
The thickness of each tread does not affect the total rise whatsoever. When the stringer is laid out, the thickness of the tread is taken off the bottom of the stringer and added on at the top when you install the stringer, so it cancels itself out.
When you put on the tread, the rise remains the same, since you add the thickness of the tread on the top of the riser and subtract the thickness on the bottom of the same riser. These two also cancel each other out.
When calculating the rise for a stringer do not figure in the tread thickness. See my article Building Stair Stringers for more information.