This has been empirically tested, although not intentionally.
The experimental guinea pig was Elvis Francois, who lives in the Caribbean islands. He was repairing his boat when it was blown out to sea with him and a bottle of ketchup aboard.
He was picked up 24 days later by a container ship after being spotted by a plane (see story here).
This is a vindication of sorts for Richard Nixon, whose agriculture department decreed that ketchup satisfied the requirement to provide a “vegetable” in school lunch programs.
This edict was widely ridiculed at the time. However, now that a lost seafarer has subsisted on ketchup, Nixon’s apologists can assert he was right all along about those school lunches. The moral, if there is one, is that a bottle of ketchup should be in every survival kit.
Related story: GOP legislators in Iowa are pushing a bill that would prohibit using SNAP benefits (aka food stamps) to purchase “meat, nuts and seeds, flour, butter, cooking oil, soup, canned fruits and vegetables, frozen prepared foods, snack foods, herbs, spices” and “even salt or pepper.” Read story here.