Hundreds of people do this every year and get jobs. For example when a person want to become a concept artist, that person receives almost NO formal education (unless they choose to go to college) someone who studies to become a concept artist has to draw and study at least 3-4 hours a day . Usually more than that.
There is a school called Sudbury valley school, they do no tests, no homework, and no curriculum. A study in 2011 showed that 80% of there graduating students went to college.(not every job needs college) And 95% was happy with there career. If someone has the desire to learn they will try to learn it. This was is my only known statistic on child led learning, unschooling, or whatever you like to call it.
Look at most mechanics. They grew up around cars. Most of them learned what they know from their parents who were also experienced mechanics. Granted most of them still go to a college or university to get a degree, but that is only to look experienced on a resume. When they went to the university or college, they basically just re-learned everything they already knew from people too terrible at the profession to get a real job. (no offense t teachers) and this carries over to many other professions as well. I had always struggled with chemistry, and my dad was always able to help me. He'd answer all my questions and leave me knowing more than i had too. School is just taking notes and getting grades and doing well on exams. Most of the things I learned, I learned from people who weren't my teachers.
I think my headline is enough evidence to show that it is possible. In fact many jobs now list the requirements to be hired. You can self learn and just straight away take the examination for the cert. Provided you are disciplined enough, it can be done and has been done.
I think experience is a good teacher. That's an old rule-of-thumb, but it is true in many things. Unfortunately, America is very much a White-collar society. If you do not have an Associate degree (bare minimum), you aren't even given a chance. Many companies require a Bachelor, as their minimum. If you cannot get hired without a formal education on your resume, you obviously cannot have a career in that occupation. Proof of this exists on any company website, CareerBuilder, Indeed, etc. -- just read the qualifications!