Of course they do.
The ones who allow themselves "independent thinking" especailly if they have an open mind....two things the WT hate.
But also as has been mentioned you get those trying to trap JW's into revealing themselves who they are and where. So be careful what you reveal.
Also as I have been reliablely informed London Bethel also monitors this site and others. Those at Bethel are worried because things appear on such sites before they even know about it, plus information which should only be available to Elders appears.
A while ago my exJW daughter (DA'd) met a JW brother while she was out one night (naughty boy he is) He has been serving at London Bethel for nearly two years and was home for a break. He said senior Bethel Elders etc, are all paranoid about what people are learning from the internet and all the information that is now available. Its making the field ministry very difficult, people are starting to ask awkward questions. Not just on paedophile issue or UN scandals. But on teachings also, why the false prophecies, why the changes in teachings, etc.
BTW this JW brother has hated his time at Bethel, he said its like being in a prison camp. You get the feeling you are being watched all the time. He will have done two years this August and can't wait to get home.