In my experience, potential employers are less impressed by education and more impressed by experience. You can gain this in a number of ways-- working on open source projects, re-designing existing interfaces, creating your own projects, or working on smaller for-hire freelance projects. What I’ve encountered is that real-world experience almost always matters more than a degree. This is largely because good UX Engineers come from all walks of life. Architects, writers, software engineers, teachers, trainers, coaches-- I’ve seen so many different people change careers successfully to this emerging skill set.
That’s not to say that education is useless or unnecessary. Before you can be successful, you’ll need to know what you’re doing. Whether that means self-study, working through online courses, or getting a degree, is up to you. I’d recommend you take the course of action that you’re most comfortable with.
Above all else, get out there and get your hands dirty!