Sure, I think an electron gas would get denser as it cooled, if other factors like the
pressure were kept the same. That's generally true for gasses. The electrons in a wire might also get a little denser as the wire cools, but only because the entire wire is getting denser. Those electrons are trapped within a crystal lattice whose density changes only a little with temperature.
However, you could never make a Bose-Einstein condensate out of electrons, because electrons are not bosons - they're fermions. That means that no two electrons can be in the same quantum state. And a system has to have a significant fraction of its particles all in the same quantum state (the lowest-energy state) to be considered a Bose-Einstein condensate.
