mmm not really cuz i think on sites like www.archive.org/ websites aren't fully archived, you may find homepages of several archived websites and their links but not the whole thing. But i believe one can create a fully functional website by ripping just the home page from archived websites and developing more pages by using the homepage as a design template.
Unless it is a static HTML you can't. If it is a Static HTML, save each page along with images in their appropriate directory.