If a new baby with jaundice went untreated, what would happen?

Varies. As many as a third of babies get jaundiced to a mild degree and it clears up over time with no treatment. In a few that develop severe jaundice the toxic material damages nerves and can produce hearing damage and a variant form of cerebral palsy. If it represents too much blood breaking down the kid might become very anemic and at risk of other complications.
Depends on degree & Type of jaundice. Mild jaundice does not leave any deleterious effect. However, severe jaundice, especially hemolytic one in preterm newborn can lead to the development of kernicterus, an encephalopathy (significant brain dysfunction) secondary to bilirubin toxicity.