The generator can put out up to 40 volts if the battery is disconnected and you don't have a voltage regulator on the generator.
If you let the engine idle at 550 RPM or less then you could briefly disconnect the battery cable, but don't turn on any lights, don't rev the engine, and don't do it for more than 10 seconds.
You can just connect a volt meter to the generator output stud and see if you get more than battery voltage with the engine running. Another way to check with no tools needed is to run the engine at fast idle and shine the lights on the garage wall at night. Then leave the lights on and turn off the engine. If the lights dim slightly, then the generator was charging.
Use an analog volt meter.