My own experience is that I never really looked at any of these forbidden sites while I was an active member. I was certainly aware of them, but I dismissed them all as being of no value. The image I had of the people who ran these sites was that of some creepy protestor you'd see standing outside a district convention with a bullhorn. I was completely turned off.
It wasn't until I started having serious doubts of my own and had been inactive for a few months that I started having a more open mind about it. I started off with some fairly innocuous searches on Google -- academic issues mainly, about religion in general. I was reading some material at a site called Religious Tolerance when I came across a truly unexpected bit of information about the Winesses. One of the topics in their outline on JWs dealt with their past opposition to vaccinations. I had no idea that vaccinations were forbidden from 1931 to 1952. That seemed unbelievable, but it was backed up by ample references to The Golden Age and Watchtower magazines of the time.
That discovery got me thinking, "what else is there about the Witnesses that I don't know?" I was disgusted and, at the same time, strangely intrigued at how people like me could be raised in the organization and not know about things like this from the past. That's when I truly began to see the degree of information control the organization uses.
Since then I've read material on many sites like Freeminds and this one. And that lead me to read the biggest bombshell of them all, Crisis of Conscience.
So I definitely agree with the point that a JW has to already be thinking critically of the organization before he's willing to even consider looking at these sites. You just don't get here by mistake. I'd say the biggest immediate threat that the Internet poses to the JWs is a lower conversion rate in the ministry in regions where online access is readily available.
And I think libra_spirit makes a very good point in his post above about the possibility of JW filtering software in the future. I think that's entirely realistic. And while it probably won't be required, it's sure to be strongly encouraged among the friends.
paterfamilias -- of the newbie class