The vast majority of active JWs that I know would never believe anything that appeared on an apostate web site if they accidentally logged on to one.
Maybe that's true of many of the most ignorant ones, but I believe that in the rest of the people there is a certain degree of curiosity. I often wondered exactly what the apostates were saying. Tell me I can't see something and I want to see it all the more. I felt confident we were right and there must be some flaw in their logic that I could find. And once I found that flaw, it would help me if I was ever confronted by an apostate door-to-door.
Yet the information wasn't readily available. I could order books, but say my father or mother saw the package and demanded to know what I ordered - I'd have been busted. It would have even been dangerous to leave it around the house too.
The internet allows a great deal of privacy from technology ignorant persons and even semi-capable ones if you are careful. You can read info on 'apostate' websites and leave no traces that anyone but an expert will find. And without those college-degrees, how many experts do they have?
I think, given the opportunity, many will check things out secretly, then it's up to them. As soon as I read my first 'apostate' literature, I was gone. And today there is so much more out there - and free. There will be those that will actively seek this stuff out, but in the end, believe it to be false information.
The internet is a severe threat. Never before has this info been so available and never before have so many left because of it. And not only do we leave once we learn, we educate others on our way out. They don't always follow us to the door, but the effect is there and the seed planted. And how many have found out the truth and still remain active JWs, subverting from within? With forums like this one to communicate with others like themselves.
Like Xander said, I wouldn't put it past them to do filter software. What's so hard about the program being written to block certain sites. The JWs could actively update the list and the software could get updated lists every time it logs on. It's not that difficult. It does send a message of control, but if likened to safeguarding us (like NetNanny does for children), the JWs might find it easy to stomach.