Not by our means or envelope of knowledge today...but neither was much of what we can do today 100 years ago.
But as discussed in another thread specifically about this...it could possibly entail some radical biological changes on our part to become beings that can survive for many nomadic generations in space...specifically without the same kind of gravity. To me, it'd have to be a big plan put in place and started at least centuries in advance as we build towards successive stages of off-world living. I think what bothers a lot of folks is the image/concept of humans becoming very different looking creatures, but it's something we very well may have to do rather than hoping for some magical teleportation or hyperspace or finding a planet just like Earth. Heck, we may look rather like octopi, but if it comes down to either that or accepting extinction, it could be yet another stage of evolution that we ourselves would induce and expedite.
Well, heh, a lot of what you just said violates basic principles of evolution, so there is that, although I suppose given enough time, a large enough ship with a self-sustained ecosystem (like a massive bio-dome) could work. However, thus far, the Bio-dome experiment has been a failure. At least the ones I am familiar with.
I won't totally discount it, but technology definitely doesn't exist in a vacuum. Most of what we've done so far is fairly consistent with what we've seen done in nature, whereas what you're talking about we've never seen done, at all. My best suggestion would be to use monoliths like those found in
2001: A Space Odyssey probably carrying both genetic and digital information to other worlds. Even that would end up being something we'd likely never know the result of, but the hope is someone with intelligence would find your monolith and figure it out.
That at least is slightly more consistent with reality. We know lifeless objects like asteroids can exist in space and travel great distances, however we know of nothing that travels between galaxies or would be able to travel between galaxies. I suppose the gravity these galaxies let off must be massive, so as one would get close to them, it'd be a sure bet things would tend to get pulled towards them, however the distances between them, and traversing them would be problematic.
The biggest problem with your idea is I know, nor does anyone else, of any life that has developed or continued to evolve in space. Space wouldn't be an environment like Earth. There's no natural selection process in space since everything would stay relatively constant (from the perspective of an organism). Whereas part of the reason we adapt to Earth is that Earth is in a constant state of gradual change. So I have trouble understand how we'd evolve to suit space travel. If you sent a population as they are now they'd probably all die off. Maybe after many generations had lived between Earth and Earth's surrounding space we'd have a few that had adapted well for space travel. Yet the distances your talking about making an all together different experience than simply sitting in a nearby space station.
We're also really coming to find out technology has a limit. Like I said, everything we've done from electricity to breaking the sound barrier seems to be replicated by nature somewhere in nature. This, not so much. Also, it seems very much that the notion of Type I, Type II and Type III civilizations is nonsense. In all likely hood if some space faring civilization existed we'd probably have found evidence by now. Because if one could do it, many ought to have considering the size and scope of the Universe and the fact that life is fairly predictable as a property of emergence. People who say "we're too stupid, they wouldn't contact us", or "maybe since we don't have space travel they're not interested", well the Native Americans didn't have a Navy, but Britain and France sure did. So it all seems highly unlikely.