No, worms cannot drown as humans do.
Earthworms don’t have the nose and lungs for the intake of oxygen.
Earthworms breathe through their skin coated with mucus to keep their it moist. This moist skin allows the exchange of oxygen and carbon dioxide directly into the bloodstreams.
When they accidentally fall into cool, clear, and running water containing a large amount of dissolved oxygen, they can survive for several days by fully submerging in water.