Whether or not someone can recover from anoxic brain damage depends on whether the anoxic brain damage was severe or moderate.
Someone who only suffered moderate anoxic brain damage may be able to recover from the brain damage while someone who suffered more severe anoxic brain damage may remain in a vegetative state or remain in a coma.
Even with moderate anoxic brain damage there's no guarantee that someone will recover from the brain damage but they have a better chance of recovering from the moderate anoxic brain damage and surviving than they do with severe anoxic brain damage.
Even when the anoxic brain damage was moderate it still can take months to even a few years to recover from the brain damage the person suffered.