Not really; it depends entirely on how the breaker is designed. The vast majority are designed to stay off until manually reset.... like the breaker's in your houses electrical service. A self-resetting breaker is the exception.
Since you mentioned household breakers, I'm replacing one of those later today. 15 amp with nothing on it but security lamp on a post. The lamp goes off and on intermittently all night long. I assumed the light sensor on top was the fault, replaced that last weekend.
That breaker is about 30 years old.