Typical car alternator, when idling, produces barely enough to supply the car's own needs, lights, etc. Even if you turn off everything you can, you may have as little as 50-100W excess, so it doesn't make much difference whether the engine is idling, or not running at all; you'll be mainly draining the battery, which, by the way, destroys the starter battery not designed to be drained.
You'll probably get your required 400ish watts if you put a brick on the pedal and run high rpm all the time, but you can imagine what the noise, fuel consumption and efficiency will be!
So yeah, a dedicated generator is really needed.