It really depends on how you learn. If you're a visual learner, and can learn from books easily then don't skip it. If you're more of a hands on learner I'd recommend a union hall to help get you started, and you can work your way up within a company at the same time. I started with no schooling and the learning curve was steep. I do not recommend it, because I felt years behind others that went through an apprenticeship at a union hall, or to school for HVAC.
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No, school is not only about learning the trade but also about opening the doors to networking for future success/opportunities.
No. Learning on the job can be great...however learning all the tech details (how things work, why things work the way they do, etc.) will make you much better at installing, diagnosing and repairing. It set you apart from those that can only fix common issues....or those that install things incorrectly because they really don't understand how it works. Differentiate yourself!
I personally advise you not to do so, unless you are a very fast learner and can tutor yourself throughout the whole process. If not, then it will only do more harm than good as you will be way behind people who actually did attend school.