No.
Brain death is _permanent_ damage to the brain. Depending on the specific definition, it may refer to either cerebral death or to failure of the brainstem to maintain functions like respiration.
It could be possible for mistakes to be made and for brain death to be declared in a patient who has not actually experienced brain death. However, this is incredibly incredibly rare: **zero** cases have been reported when appropriate guidelines are followed (Wijdicks et al. 2010). If someone is diagnosed as brain dead after a trauma, the medical staff involved in making that decision are stating that there is effectively no chance for recovery. Brain death is not diagnosed lightly.
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Wijdicks, E. F., Varelas, P. N., Gronseth, G. S., & Greer, D. M. (2010). Evidence-based guideline update: determining brain death in adults: report of the Quality Standards Subcommittee of the American Academy of Neurology. Neurology, 74(23), 1911-1918.