Although it would be technically possible:
No. The reason is simple: AddOns are meant to be a goal after you have the badge on Diamond, exept looping it. Although there are easier ones, there are also really hard ones, e.g. where you need to fulfil the Diamond requirement in a special way again. Also, most cachers will never get every AddOn, and many might only get very few. To display all AddOns would also make the badge very crowded.
All possible AddOns can be viewed here: https://project-gc.com/w/BadgeGen#Addons