Welcome to the forum!
I have a few friends who do game design and I can tell you that they suck at drawing before and after (although a bit better, but still horrible) attending a similar game design program from other universities. While AI tends to pre-screen students on their ability to draw for some degrees, I do believe that game design isn't one of them. They mostly will teach you the tools for CGI and game modeling, depending on what area you want to do.
AI is a great school and I have a few friends who went or currently go there; but they are quite pricey. You can save some money and go to a regular university or community college and learn the same thing, but having the AI alumni status does open some doors that otherwise may not be there. They have a huge community and industry access. Some friends went with CGI and did their internship out in LA, helping with projects for big box office movies like the latest Die Hard. I haven't really kept in touch with them in a while so I'm not sure how well they are doing in their careers.