The good news, is you don't lose the badges that exist in your badge box now. The bad news, is that if you have more than 1000 badges, you WILL lose whatever categories you put away for whatever the ban duration is. Additionally, if you reformat, you will lose all of you badges for good, as the possibility to redownload your badges is contingent of being able to connect.
(This could change in the future if nintendo realizes that they could let the connection go through long enough to erase everything earned, since they can't confirm what was earned legitimately and what was earned through cheating.
(This could change in the future if nintendo realizes that they could let the connection go through long enough to erase everything earned, since they can't confirm what was earned legitimately and what was earned through cheating.