Absolutely yes.
But I think the time scale set by most people is science fiction.
I think it will take many thousands of years, perhaps ten thousand years, just for the first pioneers.
Plus, where are you going to go?
Proxima Centauri, our nearest star, is 4.24 light years away, and, today, we have no reason to believe there are any planets in that system that can reasonably house or support human life.
Even our own star system has limited possibilities.
The Earth, the Moon, Mars, maybe some asteroids.
I'm not sure it's even possible to construct or anchor a human shelter on, or inside, a asteroid because of ultra low gravity.
The main issue after we solve interstellar travel is, “Where do you live?”
If you have to spend your entire life living inside a cave, I don't think space travel will catch on with the masses.
I'm also skeptical about the financial reality of mining in space.
I think if we committed $1 trillion to R&D in materials science instead of space of travel, we could probably become modern day alchemists and literally construct the minerals that have great value.
Where we would go is a question but we wouldn't have to tie ourselves to the idea of inhabiting a solar system. If we could find and utilize materials from space we could build our own worlds independent of those 'unstable' star systems.