The auto reset circuit breakers are to prevent too much current flowing thru the wires, just like any other circuit breaker. If the stalled motor current exceeded the breaker rating it should trip. Otherwise it is not there to specifically protect it.
The auto reset circuit breakers sound sophisticated, but are nothing more than a single piece of bimetal with an electrical contact on one end. When the bimetal heats enough to cause it to bend and open the contact it cuts the current to the device. But as soon as it cools, it recloses that contact allowing current to start flowing again if the switch is still being held. Each time it opens it burns the contact a little. And each burn causes it to heat faster next time.
Here is one with a burned contact. DC current is hard on contacts when they open while current is flowing as the current continues to arc across the contacts (and create excessive heat) until the space is too far for the arc to continue.
