An actual self-sufficient colony yes. We're not remotely close to that though, it'll be an outpost. Earth dies, it dies.
Hmm...
Long term, we need a viable self sustaining population of humans off Earth.
This may well take a few centuries to achieve -- but if we don't start, then it will never happen.
I doubt that a Lunar colony by itself would be sufficient -- nor for that matter, a Martian colony. The latter, because currently we have no confidence that human females can reproduce effectively on Mars (does gestation require Earth normal gravity?), nor that sufficient babies would be able to develop properly to fully functioning adults. On the other hand, I'm not aware of evidence that it can't happen either!
Pregnancy, and early, childhood may need to done in large rotating space stations to maintain sufficient g forces to enable reliably producing and raising generations of humans off Earth. I'd love to be proved overly pessimistic!
Am making the reasonably assumption that radiation shielding is a mere engineering detail, along with the necessary ability to make the space stations self sufficient in terms of air and food.
There is abundant free energy in space from solar radiation, and raw materials can be mined from planetary surfaces.
Would not surprise me that that Mercury ended up with mining camps for metals and heavy industry. There is water ice in the Mercurian polar craters, and bountiful solar energy, plus no locals will be complaining about industrial pollution!
Mars can supply more than sufficient, water, oxygen, and methane for the colony, plus probably many of the minerals it needs. Suspect that the Martian colonies collectively, will be self sufficient in terms of basic food, water, air, and fuel within 20 years. Luxury food categories may take a few more years.
I see that asteroid mining will become economically viable within 50 years, and most probably a lot sooner.
In about 200 years will have colonies on the Moon, Mars, Mercury, Venus (cloud cities), and probably other places. Also manned expeditions to Pluto and beyond.
So long as the forces of ignorance are kept sufficiently in check, but unfortunately Creationists and their ilk, are hell bent on promoting belief over understanding.