Do you think my grandma will live?

I'm assuming she has a compression fracture as opposed to a traumatic fracture with the spinal cord injury (since you mention nothing of paralysis). If so, compression fractures are fairly common among the elderly. It is often seen in frailer individuals, however, the presence of one doesn't necessarily have large impact on her overall mortality. Now, if she has had multiple falls, isn't moving well and has a myriad of other conditions, then this is certainly something to consider. Based on the information you've shared so far, I anticipate your grandmother will recover from this just fine.