Harvesting yeast from the cake will not produce lager characteristics. Those yeasts at the bottom are simply dormant yeasts that were at the top. Some yeast strains are good for top cropping, particularly English strains, because they produce a real creamy dense krausen that persists. Many American strains, though many have top cropped WLP001, do not produce a dense enough krausen to successfully top crop. In most cases the description from the yeast manufacturer will state whether the yeast is a true top cropper or not.
I like to stick to top cropping strains when I can. Its so much easier to get good viable yeast and there is no washing necessary.
(~):} Just a little Furthur (~):}