When a car or bike starter is turning, all but the engine electrical circuits are disconnected, though on some the headlights might remain on.
This protects anything that wont cope with the noise and power spikes caused by the starter motor. Running the donor car is a sure way to have all that sensitive stuff live and unprotected while the rescue vehicle starter is doing its dirty stuff.
The additional power from the generator will help but really very little - 10% more than the battery alone at best.
As said earlier battery can deliver 3,500 watts of start power. Unless the donor engine is spinning, the generator will be lucky to make 350 watts . Its not worth the risk for the small benefit.
If the dead vehicle still wont turn on jump leads, disconnect its the dead battery negative contact. If its acting like a short circuit this will allow the broken down vehicle to start. You then know its totally shot and has to be replaced.