Yes. It's possible to have knowledge without having a formal education. Oftentimes knowledge comes from having experiences and learning from the results of those experiences.
However it could also be argued that the word "educate" means to (learn) which in no way implies there most be a formal curriculum. One can teach them self how to play an instrument or learn something by experimenting. Knowledge comes with experience.
For the most part in our society will attribute education to mean a person has successfully passed a number of courses and tests. They were then given a certificate, diploma, or degree upon completion.
Nevertheless when they get a job they'll have to be "trained" as to how to succeed on that job. Real knowledge comes from hands on experience.
Truth be told there are books and classes for teaching students how to study and how to take tests.
Some specialty schools offer two week crash courses for passing tests like the SAT, Series 7 & 63 for investment advisors, State real estate and Contractor exams. Only a fool would believe just because someone passed these exams and were granted a license that makes them "experts" or knowledgeable in their fields.
There is no substitute for time, experience, and repetition to gain knowledge. Education is getting the answer right. Knowledge is (knowing) why the answer is right.