Utility and construction companies have umbrella style tents for their equipment when they are run in wet weather, so this idea has merit. The trick is building something that is easy to deploy and stow, allows ventilation and can withstand wind and snow loads.
The generator used under this cover is quiet, so additional noise dampening is really not required. If you were running a contractor style generator, I would agree to some point to add baffles. If I am boon docking, I expect generator noise. If I am in a campground, I look for hook ups to run my electrics.