If you put too little oil into the generator, it may not suffice to cover all the contacting parts with the film. This may cause wearing out too soon, as parts of the engine start damaging each other.
But if you put too much oil there, neither will it cause any good effect. Too much oil will spread through the engine, ending up in the air cleaner base and the air filter. It can result in overheating and choking out. In the cylinders, extra oil can also produce smoke, with bad results as well.
You won’t have to worry and measure oil with a pipette, though. There should be more than an extra quart of oil to cause such consequences. You can find the optimal volume of oil for your generator in the manual. It’s better to add a little more than a little less.