You CAN drown a cockroach.
You can drown a cockroach but it may take several minutes. Some experts have witnessed a cockroach survive more than fifteen minutes under cold water. Interestingly, cockroaches seem to drown more quickly in warm water. You can drown them immediately by adding soap to water as the soap stops the spiracles that block the airways from closing.
Mallis, Arnold, and Dan Moreland. Handbook of Pest control: the Behavior, Life History, and Control of Household Pests. 9th ed. Cleveland, Ohio: GIE Media, 2004. Print.
How Does the Cockroach Breathe?
The cockroach has an interesting respiratory system that consists of spiracles, a trachea, and tracheoles. The cockroach breathes in air through the set of spiracles on its exoskeleton. The air then travels throughout the body through the trachea, which is outfitted with tracheoles that exchange gas with the cells.
Petrie, Kristin. Cockroaches. Edina, Minn.: ABDO Pub., 2009. Print.