Your short answer is NO! you don't have to go to a traditional school to earn to be an audio engineer/producer. 

You can, though. If you feel that you like school and that's how you learn things. But, You don't HAVE to. 

Going to a traditional college or trade-type school is not necessary to become an audio engineer or producer. In fact, it's best if you learn from someone that knows how this is done. A mentor/mentee situation. Learning from a professional and seasoned engineer is the BEST way to learn this.

You can go old school (pun not intended) and try to just find a studio that you can intern in and basically trade labor for knowledge. This usually takes a long time, (sometimes years).

Another route is to try a mentor-type "school" that places you in a situation with a mentor to learn how to work in a studio.

That is honestly the best way. You get the best of both if you will. 

Recording Connection is one of these schools. I've been a mentor with them for almost 16 years. I have to say it is one of the best ways to learn this craft. 

They find a working studio in your area to place you with and you get to actually meet with the mentor to make sure everyone will be a good fit and then you start. RRFC is an accredited certificate school usually with a job placement assistance program for when you graduate. It is an awesome way to start your career as an audio engineer/producer.

If you work it right, you might even get hired by the studio that you learn in. Two of the guys that work here with me full time have been students of recording connection at one time or another. One guy has been working here for almost 12 years. 

When you learn the ins and outs of the studio that you are learning in. It makes more sense for the studio to hire you than someone from the outside that they would have to get used to to the studio anyway. Learn, Grow, Succeed! Basically, create your own position and fill it.

Here is a link to more information about the Recording Connection School

Simply fill out the form and one of the Recording Connection guys will reach out to you with all the info and answer any question you may have.

Good luck with your learning path to becoming an Audio Engineer/Producer!

See you on the next one!