I'm going on the assumption that if you are interested enough in teaching yourself, you have most certainly took the time to learn the physics and basics of the swing. Again, i'm talking fit, athletically inclined people who are willing to hit hundreds of balls a day and film and critique what they see have a pretty damn good chance of playing golf. If we're talking your average obese american who hits a bucket of balls twice a week, then no, they won't ever play good golf. I'm working under the assumption that the person doing this is reasonably fit and ambitious enough to practice daily, on all parts of the game, and getting in the course time to practice scrambling and course management as well.
While I have a coach, I think that the fact that im willing to put in the time and effort to become better has had just as much impact. I mean, I come from a golfing family, and I played pretty good golf before I ever got a coach (which was when I made my high school golf team). I was scratch by 18-19, and better than scratch when I got burnt a few years back and had to take almost 3 years off. Im now a 5, after playing about 100 rounds this year, but I don't know i'll ever get back to where I was. And I admit, coaching got me to scratch, and it made me more competitive, and kept my golf consistent throughout my adulthood, but I was still a 6-7 by the time I was 14 and joined our high school team (ages 14-17 here). I had never had a single lesson to that point.