Personally I learned far more from just playing around at home and side jobs that gave me freedom to program some stuff. But, as some said above, having a paper/degree counts. Especially these days, where finding/keeping a job isn't so easy. A person carrying a degree isn't a guarantee he or she will be good and willing, but employers filter out when having a wide choice of personel.
Other than that, don't forget getting a degree isn't just about learning Java, drawing flow charts, or making a robot in C++. Those are technical skills, and obviously you need some start any job. It may depend on the school, but in my case quite a lot effort was put in social / team skills as well. In practice, you work with other people. Whether those are programmers, managers, the director, electricians or a handsome secretary. Knowing your role in a company, knowing how to communicate with different persons from different professions, presenting your ideas, those are all competencies that are just as important to become successful (though you may think not, when being a younger enthioshast programmer).
Although my particular study focussed a bit less on the actual technical programming skills, it also gave me a wide view on "what's going on" in the IT world. Making games is just a sub branch within the IT business, and obviously there is a lot more you can do with your skills. Networks, websites, multi media, databases, apps, security, industrial machinery, et cetera, et cetera. It's impossible to learn and know everything in the IT branch, and of course, your knowledge will be outdated tommorrow. But having a broad idea of available techniques and such, you at least know where to search or what to look for when facing a new challenge.
As most things in life, you will carry the experience you gain from studies, hobby projects, work or whatsoever with you as valuable knowledge. If you need to follow a game course, I dunno. You could also decide to learn programming on a more global level and make games as a hobby to begin with (like I did / still do). But in any case, it's a good idea to study if you get that chance. Don't waste it.
