This is a speculation answer, but we can use the text of Night to determine some possible explanations for what would have happened if the dentist hadn’t kept the gold.
In Night, Elie is told to report for a dental inspection while he is in Auschwitz. He is confused because “I don’t have a toothache,” but he is ordered to go none the less. He finds out that the dentist is pulling gold crowns which are being collected by the Nazis. Elie can fake being sick by saying he has a fever. The dentist is perturbed but lets him go. Elie is able to avoid the dentist altogether when it is found that he has been trafficking the golden crowns rather than turning them all in.
Elie is happy because he gets to keep his gold tooth. It is likely if the dentist hadn’t been caught taking the gold, Elie would have lost his gold crown. The crown was a safety net for Elie, something he held onto to trade later on.
However, in the grand scheme of the book, the crown actually doesn’t help him much. He eventually is forced to give it to Franek, the foreman of their workgroup, in exchange for him not beating Elie’s father. Franek is friendly to him afterward and provides him with some bread, but he is transferred soon after getting the crown and doesn’t end up helping Elie much. He laments, "I lost my crown for nothing."