Nope.
Overload protection means you protect the stator coils from burning up. As an obvious example in a submersible motor it’s water cooled. Using a current simulation is a waste of time. Virtually all of these have Klixxons epoxied into the stator coils and are wired in series with the starter coil. This is an extremely reliable and inexpensive way of protecting the stator that does not need an overload relay.
Stepping up to the 250+ HP world at this point the rotor is more thermally limited than the stator. At this point typically we have microprocessor motor protection relays. It uses CTs and they are typically door mounted but don’t need to be. Some older starters use a fixed current relay set to say 4-5x FLA with a timer in conjunction with the traditional overload relay. Often these also use RTDs which are more effective than overload relays except again during startup. So it’s a “starter relay” in the end but it’s not a bimetallic or eutectic overload relay.
Finally the overload relay doesn’t need to be on the contactor. It is very common for IEC starters to use an MMS (manual motor starter) with an integrated bimetallic relay. In this configuration the contactor is optional and is only needed for automatic control. So technically we’ve just rearranged the parts. It’s not fundamentally different,
And as another Code/direction with fire pumps the wiring is oversized and they are installed without an overload relay at all. Unless the motor burns up (shorts out) we do not trip.