Leaving an injury of this sort to just "fall off" is terrible advice from a vet who obviously has very little experience with sugar gliders and their propensity for self mutilation.
If the tail is becoming necrotic, then it needs to be amputated above the site of the necrosis. Necrosis CAN continue to grow up the tail OR infect the bones and result in the death of your glider.
If the tail is not necrotic, then the break can heal and the tail might just have a little bend in it.
Regardless, the glider should have pain medications (wouldn't you want pain meds if YOU had a broken bone?) and antibiotics to combat any infection.
If an infection is allowed to go unchecked or the glider remains in pain, then the glider could self-mutilate to the point of death. Rehabilitating a glider who has self mutilated is a heart wrenching and difficult job. It is best to manage pain to avoid the prospect of self-mutilation.
You need to get this glider to a vet with more experience.
You are welcome to call me any time. 806-274-9177. I have lots of experience with tail amputation.