Haha yes, some of the Chinesium jobbies may "not be quite as robust as you might hope". My inverters here (Yaskawa and Xtravert) will trip out if the phase current exceeds the rated values entered at setup. They are supposed to protect the motor and themselves against overload (excess phase current and dissipation).

Note that if you don't implement the nameplate values (on the motor) correctly you may magnetically saturate the machine. That's more about getting the voltage and frequency right than the phase current. Saturation results in motor inductance dropping off suddenly which can lead to uncontrolled phase currents and can be difficult to protect against, whereas overload "simply" leads to overheating.