I run several dozen groups on facebook, mostly for Liberty issues or areas, some small but some with thousands of members. From experience, I think Facebook could work, but I would like to alert you all to a few issues with fb.
First, privacy on fb is an illusion. There are people watching and sometimes members receive messages about a post they thought was private, and sometimes the messages were really misunderstood by facebook central command.
Facebook groups can be harassed. If facebook does not like a group, they will make it difficult to add members, or 'lose' posts or other information, etc. Sometimes, a group just disappears. Or individual members will be harassed.
Facebook sometimes adds members to a group. Usually 'secret' groups don't have that problem, but it occasionally it can happen. These added people are trolls.
There is no provision to resolve these issues, no one to go to at facebook - there is a vague system of 'reporting' but I do not know of anyone who got a response in these circumstances.
These problems and other are rare, but I just wanted everyone to be aware that facebook is a private company with their own axe to grind, and not a neutral public service as many seem to think it is.