Is a Facebook author page a necessity? I can't answer that. But if you have one, make sure once you have 25 followers you change your URL. Let's say you're Judy, and your author page URL looks like this:
Well, once you have 25 fans or "likes", you can change that URL. I get asked about this a LOT. So, here are the instructions:
On your author page, go to Edit Page in the top right hand corner. That will take you to the "manage permissions" screen. Go to the left menu bar and click on "basic information." You should see "User Name" near the top of the page in the middle. Then Facebook will walk you through it from there. Then you can have a nice, clean URL like http://www.facebook.com/AuthorJudy.
Make sure you're happy with it the way it is, because you can't change it! And, make sure you're happy with the Name on your page, because once you hit 100 fans, you can't change that either.
Feel free to check out my author page at http://www.facebook.com/KSBrooksAuthor.