The answer depends largely upon what you mean by "spirit".

Some people break down our ecology into three parts, the soul or spiritual body, meaning the logically defined part that we point to when we talk about the person, the spirit, meaning the dynamic part that causes changes, and the mind, meaning the internal processes by which the person relates to itself and its context. Obviously, all three parts are necessary, and any two of them define the third.

Others just talk about body, the lumpy part, and the "spiritual parts", rather indiscriminately, in which case if the "spiritual parts" aren't there, then there's nobody home, so to say, even if the chemical reactions of the body, such as growing hair and nails, continue.

Dave