For all practical purposes, there is no min diameter. However, there is interaction between materials in close proximity to any antenna regardless of whether or how conductive the proximate material may be. I have seen this problem occur in many varied applications over the years installing, maintaining and operating antennas and would suggest that you consider something similar to a GAP antenna or it's equivalent which can be found with a simple Google search.
There are lots of alternatives which work more effectively than the GAP antenna as well but that discussion is beyond the scope of your question so I'll stop there.
Opinions are numerous and any generic statements usually have exceptions but all I can tell you is my own experience to not try what you described.
Last edited by k1vsk; 01-26-2010 at 08:07 AM.