In all honesty, I don't know if it would be a good idea. Big Ape is a pretty small company, and having "interns" and so forth means a good deal of supervision that quite simply we don't have the time to do.
You want a REALLY good work experience in the games industry? See if you can work the floor at E3 next May. Setup/Teardown, ushering, runners etc. etc. there's a MILLION jobs available. I have NO IDEA who you'd contact, but try
www.e3expo.com) (
http://www.e3expo.com) and see if that works.