The rubber cover is a heat and noise insulator and you'll hear more engine noises without it. It's main purpose is to keep the engine from heating the fuel tank. and frame/airbox. It is a little fiddly to get back in place, but if it's torn up, it should be replaced.
When the valves are adjusted properly and the throttle bodies are synched, noise will be minimal, but you must remember, there are lots of moving parts whirring and tapping around in there and it's not gonna be as quiet as an electronic watch.
It may be a pig, but it's a pig with a rocket in it's ass!