Well in context (medical) , "un réveil" definitely has a connotation.However the French is not clear without explanation of "un réveil" meaning "a waking-up" (from unconsciousness) of his last patient in his working life.
Source - direct link to the right page.‘I believe you,’ he said, placing his hand on Laure’s. ‘You’re my last patient. Your waking up is a good note to end my career on.’
Yes; or as suggested earlier "coming round" (from a coma); if waking-up is hyphenated, it would be used with "from a coma" to explain the different use of awakening from the everyday use of "waking up in the morning".I personally prefer "awakening" to a hyphened "waking-up", for a noun related to coma.
Otherwise, I'd leave it as a verb.