Of course it's possible to live without the Internet for a month. It's possible to live without everything but food, shelter and clothing for a month. But this is a question designed more about seeing how addicted to a behavior and source of information and entertainment one is.
Yes, I'm addicted to the Internet. We all are to some extent, anyone who is reading this. I am battling this to the extent of giving up gaming, and going back to my original addiction to books.
Currently reading: Cutting for Stone by Abraham Verghese.