As far as I can tell, one must be a published author to have an author page on Goodreads, am I right?
Sorry, I'm a little confused by what you mean so I hope I'm answering your question correctly - in general (in my experience), people use the term author to mean someone whose work is published (versus a writer who can be either published or unpublished) so if your question is whether or not Goodreads authors page is just for writers who are published, then yes-ish. Many books make it to Goodreads prior to publication date (while they are still in the production queue with the publisher (or author if self-publishing)) so you can have an author page as soon as your book appears on Goodreads, even if it's not yet published (but is in production).
If your question is whether or not authors of self-published works can have an author page, then yes, they can as well.
If your question is whether or not unpublished writers can have an author page, then no (as far as i know - someone correct me if I'm wrong) and I'm not sure why someone would want to. Goodreads is about BOOKS - the most powerful parts of Goodreads for an author are the ability of readers to shelve your book (which allows their friends to see the books they want to read/have read, which is good visibility for the book) and the giveaways (also good visibility/marketing). The author page allows you to see stats of how many people have shelved your book, are currently reading it, and quickly/easily see reviews/ratings, as well as do a giveaway. If someone doesn't have a published work for people to connect with, then a Goodreads author page isn't going to do them much good. However, everyone can still have a regular Goodreads account to use for social networking and to build friends/connections, which can be converted to an author page (and all the connections still kept) once the person becomes published.
LOL - so, I don't know if that answered your question? Hopefully, but if not, let me know!