To me, the use of the term "Whatever" in the context that I think you mean it conveys the meaning "I'm no longer interested in anything YOU have to say," in no uncertain terms. Especially if it's conveyed with a sigh and an eye-roll:
It's an extremely rude term and one that I would just as soon not hear again. I get downright angry with my students when they use that on me. (Very few have).
Cheers,