Could a quadcopter fly if its propellers were encased in cylindrical tubes?
Yes. It would be able to turn. Of your 4 propellers, 2 spin clockwise and 2 spin counterclockwise.  The torques cancel out.  To make it spin, you run the 2 clockwise propellers a little faster and the other 2 a little slower.  Now the torques do not cancel out and the quadcopter spins.  This does not change if you have a ducted fan versus a propeller