Running the generator exercises the motor and the power portion of the unit just fine, but it does not tell you about the operation of the generator.
The reason for operating it under load is to insure that the governor is working properly to maintain the specified voltage and frequency when under a load.
Operating it under load, without monitoring the voltage, is a waste of time, in my opinion. As the load increases, the governor on the motor should adjust the carburetor to insure that right up to full load, the voltage output remains fairly consistent and that the 60 cycle frequency remains within spec.
All of this can easily be checked with an inexpensive "Kill-a-watt" meter plugged in to an outlet.
Kill-a-Watt