[1]: http://www.engineeringtoolbox.com/air-altitude-pressure-d_46...
It still might not be possible, but it seems like friction would be much less of a problem. Although starting up would be a significant issue with many thousands of projectiles hitting earth at high velocity - you'd want to run it 24x7 indefinitely.
That doesn't sound like a low cost project, though; certainly well beyond our current capabilities. But you might achieve very nice energy efficiency with it.
The plasma wake will be less dense than the atmosphere displaced by the leading projectile, but it'll be much hotter and comprised of [#] much heavier atoms.
[#] "comprised of" is a correct usage, for anyone sucked in by the poor guy obsessed with editing it out of Wikipedia (many words have opposing meanings and some great English poetry depends on this; the term causes no confusion amongst native speakers; etymology is irrelevant to modern usage...)
The tyranny of the minority, in this case, is comprised of a single man, whose idiosyncratic reign of grammatical terror is now reaching out from Wikipedialand into the Greater Internet.
I find this all very amusing.
Of course, by the time we could build this (assuming its even possible), mining asteroids could already have surpassed it.
It would be exiting the barrel at far less than mach 27 so this wouldn't be an issue.
For instance, the space shuttle with SRBs and SSME's firing would require more than five Hoover Dams to match (11.7 gigawatts, vs 2.074 gigawatts). The Three Gorges Dam puts out 18.3 gigawatts, but the Saturn V first stage did somewhere around 190 gigawatts.
You could get away with less of course, since with rockets the first stage must lift the immense mass of itself, but with a railgun you will have significant efficiency losses with all of the energy conversions involved. I would expect a heavy-lift railgun to consume at least a significant percentage of a large nation's entire power supply. So we'd be looking at ludicrously sized capacitor banks, or some very large power plants that sit idle without anything to do while we aren't launching rockets.