Could use an importer app to move a web site to Site Designer.

This would be virtually impossible given the many types of sites developed with many types of frameworks. It is probably the reason why it has not already been invented. That being said once you learn SD3 it is extremely easy to recreate your old website. There are lots of folks in the forums that can help if you get stuck along the way. Coffeecup also has lots of written and video tutorials available.