If that is what you want to do, your target should be to work for small companies, like @60Six mentioned. With fewer employees at hand, being able to do multiple things is extremely helpful. I myself have worked as a graphic designer and illustrator for many companies.
You can build two portfolios when going into the job hunt. Both should be great of course. When arriving at an interview, being able to mention your additional abilities can be a plus for certain companies.
There is a downside too: Being unfocused. I have met many who want to do a lot of things, but don't do any of them well. It can make people feel like you don't know what you want in your career. That is a huge problem for an employer, usually resulting in not hiring a candidate.
You are in school still and I'm guessing you are interested in both jobs. Go ahead and pursue studying both then, that is what school is for. It is very possible that after a couple months or years working on various projects you realize where your passion truly lies. And if it is both animation and game design, that's fine too.