My misunderstanding ... I read "biography box" in your original post as the default, WordPress core, biographical details text box, not the "short biography box" that the current version of WP Biographia adds for the plugin's widget.
So this is the current state of play ...
In an earlier iteration of what will become the next version of the plugin, v3.3, I added some code to hide the short biography in the user's profile if the plugin's widget was not currently active in any sidebar.
But then I got a feature request to allow both full biography text as well as excerpt biography text in the rendered Biography Box, configured on a per-post basis.
So now, the short biography text is back in the user's profile, but it's renamed Biographical Excerpt, with the following description
Share an excerpt of your biography which can be used by the WP Biographia shortcode, template tags, sidebar widget and configured to be used in place of the standard biography for differing template types.
... which I hope is more descriptive (sadly I can't change the default biography text description of "Share a little biographical information to fill out your profile. This may be shown publicly" ... this isn't able to be amended/filtered.
Now I can keep it like that, or I can key in on a new plugin setting which appears on the Admin tab of the plugin's settings which enabled per post specific overrides, although I'm mindful that removing the biography except when it's not being used may in turn cause further confusion.
Hopefully this makes sense ...