No, cargo containers are not airtight if submerged underwater. They are designed to be watertight but have doors and vents that compromise airtightness. Under extreme water pressure, those openings eventually fail, flooding the container.
The timeline depends on factors like depth and container strength. But most will flood within hours or days once submerged.
Flooding damages or destroys container contents and the container itself. It also pollutes surrounding waters.
To prevent this, ships must securely lash containers to deck. Monitoring weather and avoiding rough seas helps too. With proper precautions, ships can prevent cargo containers from falling overboard and flooding underwater.