There's more to the internet than what you see when you use a web browser. For example, all telephone switching systems are routed over the internet - ALL OF THEM.
That's just one thing. The real question should be rephrased as one that asks if a individual could not use the internet not if it was somehow - can't happen - everywhere.
So yes, as a individuals, some of us could do it but not all. I for one could not since I'm a Systems Analyst and not having internet access would be like trying to learn how to scuba dive without water. You know because Self-Contained UNDERWATER Breathing Apparatus, literally exists for the presence of water.
If this was a question asked back in the late 80's you might have a good reason and ability to not be affected by the internet. But today, you cannot live without it, even if you don't directly use it.
Unless you plan on moving to a rainforest to live in a hut made from feces and leaves you can't live without it either.