Is BIID life threatening?
It can be.
People with Body Integrity Identity Disorder are already disabled, and for some, the desire to be an amputee (or whatever) can become so intense, debilitating and depressing, that nothing else matters. It can reach a stage where the desire to be rid of the limb can focus the mind to the exclusion of every other aspect of life. This is a critical time, as the sufferer may resort to dangerous and life-threatening self-harm to resolve their despair. While the focus is on the desired transformation, the sufferer is usually resigned to the possibility of dying in the attempt, and proceeding regardless.
That said, it would appear that a proportion of individuals with BIID do not reach that state of desperation. But, the nature of BIID and its reporting is such that any discussion of 'numbers' is wild speculation.
If a surgical alternative was offered, the people requiring a surgical solution would not need to risk their lives by attempting self-injury.