Absolutely! If you have real passion and talent, qualifications aren't all that important. I suspect you'd be hard pushed to find a UX professional over the age of 30 with a college degree in UX. People come from all over the place to this profession.
You have nothing to lose by applying. Plot a path that includes education and experience, and apply for jobs all along the way. Build a portfolio, take on volunteer projects, offer to intern for free (if you can afford it) – just get out there and get your hands dirty. Employers are going to value enthusiasm and a great work ethic as much as a formal education.
You don't need to work with a UX team. Go to your local school, museum, or community group. Offer to do pro bono work in return for using the project in your portfolio. You need project experience and portfolio material primarily.
Does that help?