Circuit breakers are on the hot lines, there isn’t a case where high currents “bypass the breaker” (except for a bad install, which for this specific scenario wouldn’t have anything to do with whether the neutral is connected to earth or not).

AFCI and GFCI breakers will care about the return path, but that is in addition to normal circuit breaker “does this exceed the current limit” behavior. And it is a very important reason not to connect the neutral to ground at the appliance level