Creating an option for writing a post without an author attribution for a group blog on WordPress

This is entirely possible. Though, I would recommend using the Post custom metadata (i.e. custom fields, or better yet, a custom metabox).

I would use a custom metabox, with two radio select options:

Byline:
(*) Author
( ) None

Then, in your template file, you can output the author byline only if the appropriate post_meta key has the appropriate value. If you want to get really fancy with it, you can even use the post_meta key/value to customize the Loop for your Author archive index output, so that Posts indicated not to display the byline don’t output in the Author’s archive index.