|MadSci Network: Zoology|
Very good question! To my knowledge it has not been specifically studied in a laboratory setting, but would be very easy to test. If the spider web was wet it might conduct electricity, but in general I believe not very well and only by ionic conductivity.
Also, the spider would not be electrocuted for landing on an electric fence for the same reason that birds are not electrocuted for landing on powerlines; they are not grounded. Electric fences work the same way. Animals (and people) get shocked because they are standing on the ground. Only 10,000V fences would be a problem when she grounds her web.
Additionally, the spider silk is composed chiefly of the amino acid alanine, which is non-conductive.
Incidently, spider silk is considered an optimal fiber for new materials, because it is tougher and stronger than currently available fibers (like KEVLAR). In fact, it's being studied as a possible suture for surgeons.
For more informiation, check out the following spider sites:
Spider Silk Sutures (http://wwwmed.stanford.edu/medworld/doctalk/ spidersuture_lc.html)
Spider silk strength (http://www.xs4all.nl/~ednieuw/Spiders/Info/spindraad.htm)
European spiders (http://www.xs4all.nl/~ednieuw/Spiders/spidhome.htm)
Australian spider page (http://www.xs4all.nl/~ednieuw/australian/Spidaus.html)