Yes, definitely. All motors, for example, have a starting surge current much higher than their steady state current (a factor of 6 to 10 typically). So breakers are designed to trip quickly at very high current, and more slowly at lower multiples of their rating.
You can look at an example of a breaker trip curve in, say, page 2 of this document:
Say you had a 30A breaker that follows this curve. If I look at the 100s line, I see the graph specifies a tripping current of 1.4x to 2x. Meaning that the breaker is supposed to take longer than 100s to trip when the load is 40A, and is supposed to take no more than 100s to trip when the load is 60A.
Of course, that graph is just an example, the manufacturer of a particular breaker should have a more specific document with the trip curves for that breaker. The listing standard for breakers, UL 489, probably provides upper and lower bands for breaker trip curves, and that document may be using those bounds, I didn't look at it closely to see.
Cheers, Wayne