Yes! Deep learning is a young field. I have a B.S., for example, and have published work at Interspeech (speech recognition conference) and NIPS workshop (machine learning conference). You can too.
My advice:
* 80% of machine learning is software engineering. If you're a strong software engineer, with some good math foundations (calculus, probability, matrix algebra), you can make significant contributions.
* For deep learning, you can start with the crash course, but you'll eventually want to read a full textbook. If you read the new Goodfellow, Bengio, and Courville textbook and understand the details of the algorithms, then you'll be up to speed with the major ideas in deep learning today: http://www.deeplearningbook.org/
* Find a company with existing deep learning experts who need software help -- that's most companies applying deep learning.
* Read research papers. Some will be easy to read, some will be hard. If they're hard, read the references they cite. Eventually they'll get easier.