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Rogue planets come within a few light years of Earth. We could probably have a low speed, multi-generational ship to intercept one in a few hundred years. Once we're on we're hopefully good forever. Likely we'll come close enough to some other interstellar bodies we could populate as we travelled. Exponential growth is bound to take off.
Yeah, if we aren't in a hurry, and we can set up some fusion reactors and such on them and build whole civilizations on these rogue planets in the dark, it would work. Depends on how early and often we set up shop on passing planets, but in theory we could colonize much of the galaxy in a few revolutions around the milky way. So, under a billion years. ;)
I'm guessing if we've reached a level of tech to build a functional generational ship we would be patient.