As an Intern myself, I think I might be able to provide some insight in this area! I cant give you any information on the hiring of interns for departments other than Community, but I can say that applying doesnt hurt.
I am currently enrolled at USC in the Masters of Communication Management in Technology and Online Communities program. We need internship credits to graduate, so I figured, I should go to PAX and try to speak to some Rioters in person. I was told to send in a resume and cover letter and eventually was hired. I would encourage you to apply! Try sending the required documents to your department of choice and let them know youd like to apply specifically for an internship and see what happens!
You can find the emails for each specific department here