I don't believe that Facebook groups do anything to further any cause at all. I believe this because I myself belong to 2,487 different groups including 'Democrats who think Obama is swell', 'Heterosexual Men in support of Women!' and '1,000,000 people against masturbating with exfoliating soap'. So far, very few of them even acknowledge my existence let alone give me any information to work with.
Let's put this another way. In some parts of the world, people get active and take to the streets to protest villainy, corruption and oppression. On Facebook, we click a link, get warm and fuzzy and feel that we have accomplished great deeds. Don't like Cancer? Join a group. Dislike Senate Republicans? There is a group for you. Hate Clay Aiken? Let him know by lining up with like-minded group members.
Facebook groups really do nothing to further any cause, policy, debate or malady. They simply allow a small conversation to begin:
"Hey, Bob, anal leakage really sucks doesn't it?".
"Yeah, Bill, it sure does".
And sometimes not even that much.
It is the online equivalent of staying at a Holiday Inn Express last night.
To be fair, though, I do have a couple groups that do, at least, try to keep me informed. The recent group formed to get Facebook to revert back to their old Terms of Service actually worked and showed what these groups might be capable of. Likewise, 'Hey Facebook, breastfeeding is not obscene! (Official petition to Facebook)' might be able to change the way the site views these type of images. '25,000 in Wisconsin to Re-Elect Chief Justice Shirley Abrahamson' keeps me up to date with everything that is happening with this vital campaign. And being involved with 'I bet I can find 69,000 People who Hate Nickelback' is just a no-brainer.
So, to answer your question, while Facebook groups can help a person feel like they are connected, involved and informed, they actually do not do much of anything. I mean, I know what exfoliating means now, but I had to find out the hard way.