Indeed, Clarice has a very short history for the reputation she's obtained.
Her sole appearance in a Disney cartoon was in the Chip 'n Dale animated short "Two Chips and a Miss", released on 21 March 1952. In the short, she invites both Chip and Dale seperately to a clandestine rendez-vous with her. When they encounter each other, they bicker over her affection before eventually making up.
While she is not very well known in the United States, she is extremely popular among the Japanese, and to a lesser extent among Europeans.