Is wire-wrap for components, or just special boards and pins?
I talked to a tech at Jonard, which has made a lot of these tools.  He clarified the following:


Wrap wire does not need to be plated.
The diameter of the wrap tool or bit can't be very much larger than the diagonal of the wrapping post or else the wrap will not be tight.
Wire wrap was not designed for it, but if you can match the wrapping bit to it you can wrap a round conductor and it will make a good electrical connection.  But you would then have to solder or mechanically secure the wrap from sliding off the end.