Not currently, but that's an interesting idea.
I'm new here and was looking for this feature, so I did a search and resurrected this thread rather than posting a new one.
I'd like to see this implemented. The medal wouldn't have to show up on a roster but rather on the character view. Seems like the easiest way to implement this would be to create a new type of custom field for the character profile. The field would have to allow for a title and graphic so that you could input a picture of the medal and the name of the medal.