I would say it depends on the person. Can you live in your own country without Internet? The answer should be the same.Is it possible to stay in Japan and without an internet connection? Or is it going to get bored without the internet?
Indeed. I did it the old-fashioned way. I took classes with textbooks in college. Did self-study using print materials. And lived in Japan where I used a private tutor. The extent of my electronics was using an electronic dictionary from Casio called a "WordTank." Even then I didn't make it to JLPT1. Once I got good enough in everyday conversation and living and got busy with work and life, studying to pass a test became less of a priority for me.I mean people did took JLPT before there was internet, right? Or before there was internet, people did learn it through other source of methods besides internet.
Probably because the people you are with have one. It would be hard to go back to a truly non-connected life.People tell me all the time that I need a cell phone, but I seem to be doing just fine without one.