How essential is vitamin B3 to the diet?
According to one study:


  It was calculated that if the excretory percentage of niacin metabolites in the urine were 60%, of the tryptophan ingested, the conversion factor would be a value of 67, meaning that is 67 mg of tryptophan is equal to 1 mg of niacin.


However, the study has a pretty low power with only 10 participants and an indirect measure of niacin.

Is it possible that a person could get all of their niacin from tryptophan? Probably - you just need to eat enough tryptophan, which is also an Essential Amino Acid. The body may preferentially keep Tryptophan (which it does not store) until Niacin runs out (which also cannot be stored).