Answer: Not sure but here are my thoughts.
Explanation: This isn't exactly verifiable but here is my best guess.
You burn through your stored carbs in about a day. Normally the body would then switch to burning its fat stores, but without ketosis I am assuming in this hypothetical the fat-burning stage is skipped entirely.
I don't know if burning the body's protein and other structures is part of ketosis? If it isn't then you may have another couple days or so where the body literally eats itself, but it won't last very long if you have zero fat, which I'm assuming would have to be true if the body couldn't do ketosis.
Also, is disease a factor? Apparently death through starvation normally ends due to disease, as said here:
"Few people die directly from starvation because they usually die of an infectious disease first. Starvation wreaks havoc on a person's immune system, largely on account of an extreme deficiency of minerals and vitamins. Some people will become weak and perish of immune-related diseases during starvation. Eventually, the person's body will run out of options. Fats, glucose, muscle mass and tissue are finite resources that will eventually be spent and the person will die. The end-stage of starvation usually brings with it one of two different diseases - kwashiorkor and marasmus."
Summary: It is hard to get an exact number of days. I would guess less than a week, but there are more factors than just ketosis. Considering body type, water access, and disease, it could be longer or shorter.