It may not be the most elegant of solutions but you could have 2 dropdowndivconverters, set a different image for them and then set the visibility settings either on User roles.
Drop down one has sad face image and is only visible for the Guest user role.
Drop down two has a happy face and is only visible for the User user role
Branden has a good point if you have a limited number of images to show. If you actually want a specific user’s image or avatar, I think the DropdownDivConverter widget would need to be enhanced. It’s open source on Github here: https://github.com/mendix/DropdownDivConverter