If you use the supplemental training for learning, then you'll get the practical benefit of it. Doing a supplemental course in something closely related to UX may give your potential employers some confidence that you have a real interest in the field, but I wouldn't rely on the qualifications for this.
As Hawk says, it's very much a personal network and portfolio-driven thing. Just as you'd have a showreel for animation of media, UX has a kind of portfolio. It's fundamentally different from a typical graphic design portfolio though - it focusses on showing process, research findings and design thinking rather than just the pretty end result. A massive part of it is proving that you can do the job - backed by skills, experience and aptitude. Here's an article I wrote about UX portfolios: http://uxmastery.com/10-steps-to-a-perfect-ux-portfolio/
Most experienced UX designers won't have done a UX degree as they've only been available recently. As a result, many employers (not all) don't necessarily look for the qualifications first.
Because I'm self-employed, most of my UX gigs are project-based and contracted. I've also worked in-house across multiple projects. Some people work as part of a UX agency, employed full-time but across multiple projects. Others work in-house on a single massive project for years. As Hawk says, it's really up to you what kind of role you'd like to go for.