Have you tried copying the content of contrib/auth and placing it in a directory in your app? It should work (perhaps with a bit of tweaking) BUT you will have to be careful where they both use the same data (for example the setting for the login url) and may have other problems.
I cannot see what possible benefit you will got from this, and it is probably the wrong thing to do. You should almost certainly either:
2) create a model within your app with a onetoone field pointing at the user for extra information