Home Building: Do the first and second floor exterior walls have to line up?
I’m not sure what you are saving: 1) Roofing and roof structure? 2) Walls? 3) Second floor structure? 4) Foundation?
5) Heating?

1) You will have the same amount of roof structure, except it will be divided with some on the top of the first floor and some on top of the second floor. In addition, it’s more complicated (and expensive) to tie the lower level into the second floor wall and flash it properly. 

2) You’ll have a few longer walls. This wall area will require a finish on the interior and exterior. 

3) The second floor framing will need to be larger in order to support the second floor walls and roof structure. 

4) The foundation will need to be the same size and support the same amount of roof load and nearly the same second floor - floor load. No savings. 

5) You’ll save a small amount of space heating, but insulation will be more difficult to install and not as efficient.