Not quite, IMHO a katsu dish still has to have meat in there somewhere. For your examples:

肉巻きカツ is a meat roll katsu wrapped around an egg.

串かつケーキ is not a kushi(katsu cake), it's a (kushikatsu) cake. While it doesn't contain any meat, it's named after kushikatsu, an Osakan dish of deep fried stuff on a stick.