Can I connect unused ceiling fan wire with neutral?
It was common to wire "switch loops" where a black and white wire were run between a switch and a light, and the white (neutral) wire would actually be used as a hot.  When this was done, the white wire would be marked with black tape on both ends to say "this wire is really doing the job of a black wire".  (wire colors are assuming common US conventions).

What you are proposing is doing something similar, but using a black wire as a neutral.  This will work, but according to another question you can't repurpose a black wire as a neutral because code requires a neutral to be a certain color over the entire length of the wire.

So, electrically, it will work, but it seems to be an illegal modification.