Possible, but quite difficult if you want to write a generic application
that users of Outlook in any configuration can use. Such an application
would need an ASP.NET custom control with client-side JScript to manage the
interaction with the address book component in Outlook, an interaction that
will itself trigger security prompts. Not fun at all.

If you're working in an Exchange environment, though, it might be
interesting to see if anyone's done any work in using WebDAV to generate
something that looks like the OL address book.