Generally speaking, as in not games developer specific, it would be a very good idea to get that degree. If for no other reason, then to show that you've got what it takes to be in that line of work.
I started out as a self tought and it was all very nice, except that I had to work twice as hard as people with a paper to get recognition for what I did. Later in life, I went back and did my CS thing, and that was the best move in my life.
Not only did it open my eyes for a completely different world, but it also taught me the naivite of my previous work.
Today, I have the benefit of age and a network of friends in all the right spots around the world, no small part of whom are buddy's from the university time.
And that's just the social and and employment potential benefits.
From a purely professional point of view, self taught people tend to very limited in theit "skill palette", they are very good at what they are interested in, but they are not very flexible when it comes to working on even related tasks. I know this, because I've had to let a few people go every now and then (mostly self taughts), they simply were not flexible enough. Specialists are very good for contract jobs, but not for permanent employment.
For me, the most important lesson learnt, was the skill of aquiring new developer skills. Something that might require a different mindset than the "untrained" mind.
Getting a formal education definitely broadens your horizont as a developer, games developer or not.
Just my 0.25$