Space colonisation will never help with Terran overpopulation. That's a problem that needs to be solved internally, and it's either Wisdom or Malthus that's going to do it. It's only progress (social, intellectual, or technological - likely a combination of all three) that can solve this.
What space colonisation will do is change the relative ratio of Terrans. I've commented before that only 93% of all human adults have died - it's far from certain that 'death is certain' in the time-frames we're used to. Likewise, we think of Earth as being human. But, if we play our cards right, Terrans might end up being a tiny subset of total people.
Thinking about it a bit more, I must concede that space colonisation won't solve overpopulation.
Who needs a life when there are video games? (And Warhammer)
Orks: 2000 points