Well, undrinkable only when the sea water is not being treated.
Many of my friends and I had the experienced of drinking sea water that has been 'converted' to a fresh water while we were at sea when serving the navy onboard Mine Counter Measure Vessels (MCMVs) some 30 years ago.
These ships are equipped with the 'machine', that purifies sea water known as reverse osmosis water purification system. It doesn't taste good then. But over the time this system has since improved tremendously to the extend that sailors are now being able to work at sea for relatively longer period of time without the need of tap water.
Just a thought.