Opinion is divided on that one, Ken.
Ballpoints don't feed by gravity, the feed by capillary action. Most won't work if held upside down for any length of time because the -1g tends to pull the ink away from the ball and, once separated from it, the ink loses its capillary action. Zero g is a different matter. There is no force to pull the ink either way so the surface tension can do its work.
One of the astronauts on ISS (or was it Space Lab?) tried it with a ball point he nicked from NASA and reported in his blog that it was working fine.
That said, if the 50c biro stopped working they wouldn't be able to do their homework any more so the space pen is certainly a safer option!