Regionals don't care about a degree, just a pulse and an ATP. Majors have tens of thousands of apps on file and do require or highly desire a degree. You'd be at a huge disadvantage without one. It doesn't have to be a $100,000 certificate from ERAU or one of the other pilot factories. Any degree from a properly accredited school will check the box. Ideally, it's best to have a degree in a real field completely unrelated to aviation that you can actually use during your eventual furlough at some point in your career.