I'm not currently in school, but I can speak to past experiences.
In high school (2003-2007), we formed a GSA (Gay Straight Alliance). The membership was almost exclusively gay guys and lesbians and every now and then someone would bring a straight friend. We couldn't find the required faculty advisor, and therefore never really accomplished anything. After the first year, we only had one or two meetings per year. Overall, ineffective and a waste of time. We didn't do anything with the rest of the school and the only people who regularly attended were all friends, so we weren't educating anyone else.
In college (2007-2011), I joined the Pride Alliance for LGBTQ students and allies. My university had 30,000+ people and a dedicated LGBTQ Student Services Office, so there was a fairly large turnout. Every weekly meeting had an educational topic and was accompanied by introductions and an after meeting meal. It was excellent for making friends, finding dates, networking with friendly faculty and staff, and learning about topics relevant to the community. After the first year that I was a member, the issue was raised that there wasn't very much trans representation in the meeting topic choices. They made an effort to be more inclusive, but ultimately a separate trans group was formed. I never attended this one, because I wasn't out yet. Overall, they were very involved in the university's culture, very education-focused, but were more so interested in educating our community on topics of internal interest.
I think the issue with assuming the presence of these groups = education and safety is the bubble that they tend to find themselves in. Who are the people we want to educate? Everyone, especially those that have no exposure to the community. Who is least likely to come to any kind of function put on by one of these groups? People who have no exposure to the community.