Does a conductor that is heavily negatively charged affect the number of free electrons or conductivity?
Back-of-the-envelope fun:

According to http://en.wikipedia.org/wiki/Capacitance#Self-capacitance, a 20-cm radius sphere has a capacitance of ~22 pF. If charged to -1 MV, it would have 22 uC of charge. A coulomb is about 6E18 electrons, so there would be about 1E14 extra electrons on the surface. The area is about half a square meter, or 5E17 square nanometers, and each square nanometer would have (very approximately) 10 or so metal atoms exposed.

So, even accounting for the fact that all the extra electrons would go to the surface of the conductor, even really high voltages would add on average a tiny fraction (about 1/50,000) of an electron per atom to the "electron soup" of the conductor. 

I'm not a physicist, but I wouldn't expect that to make much difference to the conductivity of the system.