Unfortunately I have another non-success story, but I've read plenty of success stories here on CB, so don't loose hope.
For us it didn't end well. DD was diagnosed with a L5 stress fracture. We did everything the doctors told us to do - rest, brace, PT, etc. It healed nicely. In fact, the doctor was very happy with the way it healed, because as
@gymmutti said above it usually heals as a connective tissue, but in DD's case it actually healed with a bone.
She went back to full gymnastics, but 6 months later the pain came back. The diagnosis was stress reaction at the exact same spot. Whatever caused her fracture at the first place wasn't corrected, so as she went back to gymnastics, the stress came back. This is to say that just to heal the fracture is not enough. You have to find a good Sports doctor or PT or someone who understands gymnastics, and can figure out what caused the injure and help to correct the underlying issue.
In my DD's case, after the injure re-occurred we tried everything - rest, back brace, lots of PT, stretching hips, shoulders, strengthening core, etc., nothing helped, the pain wouldn't go away. The follow-up MRI showed "degenerative facets", which basically means that the facets (joints between vertebrae) are permanently damaged. The doctors assured me that people can live with this condition and do sports and be active. As long as DD can maintain a strong core to support her back she should be pain free.
That was the end of gymnastics for her though. Now 1.5 years later she finally doesn't have any pain, she dances, plays softball, etc. But unfortunately gymnastics is out of the question for her ever.
But again, I don't want you to be discouraged. Do a search here on CB for "stress fracture", and you can find many success stories.