I guess her name is Sugar and she is self diagnosed. While self diagnosis is not a problem, (some people don't have the resources to get a proper diagnosis) I guess she's using it as an excuse to be really awful to a lot of people.
Yes, the character claimed to have "Self-diagnosed Aspergers" and used that as an excuse not to self-censor. She thinks that will let her get away with being just plain rude. However, now that she's "in" the group (although she cannot sing well, she can dance okay), she has toned down that behavior.
No one ever portrayed her as really having Aspergers.