There are many people who pursue a TEFL career and they come from all walks of life. There are those who've done their PhDs and worked in research fields before jet setting to foreign lands for more fun and enticing jobs while there's an equal number of folks with just a high school diploma, who've been stuck at a dead end and see a TEFL certificate as their saviour. The good thing is TEFL does not discriminate and you can obtain your certifications regardless of your educational qualifications as long as your English language skills are of good standards.
However, that doesn't mean your educational degree holds no sway when in comes to employment though.
Sure you can walk around saying that bill gates and mark Zuckerberg don't have a degree either, but you'll quickly find that many employers don't hold that kind of argument in high esteem. Like with every other profession, the value and significance of a college degree depends largely upon the country you choose to work in and the type of job profile you get.
In fact, just to get a work visa in asian countries like China, Japan, south Korea and Vietnam, you need to hold a bachelor's degree. Without it, you cannot legally get a work visa meaning you can't teach English for a living, or even reside out there for long by doing odd jobs. Even if you have years of experience, or are an exceptional talent, the government regulations are strict and there's no work around.
But your Asian sojourn doesn't have to end here though. There are countries such as Thailand and Cambodia which accept TEFL teachers with valid certificates even if they don't have a college degree. The cost of living is much cheaper here and good prospective work does not stress on degrees but the amount of experience you have.
Away from Asia, the situation again varies widely depending on the location. South American countries like Brazil, Colombia, Mexico and others on the western hemisphere rarely stress on college degrees. European countries, especially western Europe though, are notoriously difficult to get into even with a college degree "and" good TEFL certifications "and" experience while eastern European countries work along the same protocols although they stress on your TEFL certifications more than your educational degree.
Of all the places in the world, no region is more stricter with regards to your educational qualifications than the middle East where a degree from a reputed college is paramount to even getting a visa.
In short, although you can work in many countries and even go far in your career path without a college degree, you do get a leg up if you hold one. You can leverage a university degree along with reputed TEFL certifications to magnify your job prospects and get your foot in the door among big name organizations and top notch institutes, which otherwise might be closed to you. But at the end, it all comes down to how good of a TEFL teacher you are.