Not quite, the thermal element is effectively an integrator with the temperature increasing at a rate roughly proportional to the square of the current; a relatively small overload may take many minutes to trip the MCB. For large overloads the breaker must trip very quickly, and the magnetic circuit is responsible for this.
For covering loads with different inrush currents the magnetic actuation is available with different trip limits, identified by the MCB "Type" e.g. Type B, Type C, Type D etc.