The phrase can sound dismissive or curt, showing annoyance or impatience towards the questioned suggestion. Would you ever cheat on the test? Of course not!
Pro Tip 2/3
Emphasizing Certainty
Use it to make your negation very clear and to show there's no doubt about your response. Is your business failing? Of course not, it's doing great!
Pro Tip 3/3
Informal Setting
Most appropriate in casual conversations rather than formal or professional communication. Would I skip your birthday? Of course not!