Of course it will depend on the type of internship. Sometimes animation students get internships doing PA type of stuff in companies that are not so great... I mean, if what you really want is to animate you probably won't be happy making xerox copies or going pick up dinner for the boss. This type of internship will probably not turn you into a better animator. It's true though that getting an internship in any of the big studios, even if it's not exactly in production, can be a nice way to get a feeling for how it all works, and also to get good connections and some professional experience. So it all depends on what is the internship like, and in what company.
The best situation is to get an internship where you can develop your skills as an animator and artist, and in a good studio. This type of internship is a wonderful way to start a professional career. Well, at least it worked for me! I was an intern first at Briquet Studios in Sao Paulo (2D), and then at Rhythm & Hues Studios in LA and these two experiences were crucial to my background. At Briquet Studios I was lucky to be an intern under the supervision of Renato dos Anjos – he later ended up moving to the US and worked as supervising animator on Bolt, Surf's Up and Open Season. I knew nothing about animation at that time, so it was really my very first experience, a way to get a feeling for how it all worked on a professional environment. The studio was really small but their work was great, Renato was really good and I learned so much from him. It was not enough time to get good at it, but I felt the experience planted the seed of animation on a fertile soil.
A couple of years after that, I went to School of Visual Arts in New York for my master's degree. During my first summer vacation I got an internship position at Rhythm & Hues. It was amazing. I felt I learned more in this time than in all my time at school! Rhythm & Hues had classes set up for new employers and interns, it was very organized and that's when I really started to understand what 3D was all about. I learned so much. I came back to school after the summer full of energy and started working on my short film. I also met a lot of really nice people, made important professional connections and went to a couple of cool camping trips. Fun times!
So, based on my personal experience, I think a good internship can help turn a student into a good professional. I was lucky in that my internships were really about the animation work. They were also at good companies with a solid reputation. It was a real learning experience on many levels.
Some of my students get internships and I see how positively the experience affects them. In many cases, a company offering an internship program has hopes that that student will be a possible hire in the near future. In a way, you are being “tested” by them, while at the same time you will be learning tons of useful things. Some companies have a very structured internship program – they put a lot of thought into it, and these are the internships you should definitely apply for! Here in California I know that Dreamworks, Pixar, Disney and Rhythm & Hues all offer this type of opportunity. And I bet there are other companies with great internship programs that I just don't know about.
Of course it is not exactly easy to get an internship at one of the best companies in the world - they are very competitive programs, but these would be the first ones I would try if I was a student now. I know it sounds hyperbolic, but it can be life changing to spend a summer working at a studio like any of these. You will meet amazing artists and professionals. You will get to know how the pipeline works, how is the day to day of a CG artist, how the films are done, what the work ethics are like. You will learn about work flow, techniques and art, and you will learn it from real artists. It can make a real difference in your career.