Hiding custom avatars

How can I make it so that no avatar images are "public" when a user has not registered/logged in?

We have a community where some KB content is public, but some KB content and all our forum and blog boards are only available to our customers. I want to know how to set all avatar images to "Hidden" rather than "Public".  

Example: Customer uploads a photo of themselves and sets that photo as their avatar image). We want it so that no unregistered or logged out users can see that avatar image, but when the user logs in, they can then see avatar images.

I've found the avatar settings and have set them to no show avatars at the community (and then set to show them at the category and board levels) and that works to limit when the avatar image is visible, but it doesn't prevent an unregistered user from seeing the image if they locate the user and view that user's profile. The image won't show up as the avatar on the profile, the the images section still has the avatar image as "public".