Definitely doable. But then there's no longer any special appeal to living on Mars, as opposed to: living in rotating space habitats among the asteroids.
If we reformulate Musk's goal as being: "Create off-site backups of human civilization", then I think asteroid mining & space habitats have a better shot at bootstrapping this process than colonizing Mars.
Once we are leveled up this way in resources and technology, building settlements on Mars can be a side-effect of this outcome. Just like the burgeoning scientific outposts on Antarctica are a side-effect of our current civilization.