Picture a standard quadcopter, with regular old propeller guards, which are generally just circles around the propellers. Now, take the propeller guards and stretch them so that they're cylinders surrounding the immediate cross-section of propeller blades, as well as some distance above/beneath them.
Now I am fairly certain that it would be able to go up/down. But would it be able to turn? I know it is a relatively vague question, but after thinking about it for some time, I really have no idea. I might just modify the propeller guards on my cheap little drone to see if this works.