Yes but it is not a quick process. Your process of how natural linking is done to day is not quite right. You need to write great content, have real people share it socially, that then attracts the attention of those that would link to you, then you gain rankings.
If I was to start today, I would start by building my Facebook and Twitter following as fast as possible, including advertising for fans on Facebook. You can get them for as little as a penny a piece if you do it right. When you get over 20k, you start having social clout which makes other people link to you if you write good content. I get dozens of natural links per day from twitter papers (paper.li) other blogs in my niche, and I now have two major websites in my niche PR5 and PR6 who syndicate the posts I choose that include attribution links and anchor links. It took 1.5 years to get here.