Do you think it would work if I (or anyone for that matter) made a Facebook or twitter about their forum and started friending and following random people?
You need to target certain people as depending on your forum niche . For example a gaming,music or general forum could have big success that way because there are a lot of gamers and I have never heard about a person who didnt listen to music. In other genres you must find people related to your forum niche.
It works for me on Facebook. I rarely go on Twitter, and received only a few visitors from them. I got 172 likes on my fan page for my forum, and several friends related to my niche.
Focusing purely on a forum and no promotional aspects for it doesn't sound like a good idea to me. People won't visit a board if they don't know it exists, regardless of how good you make it.
I created a facebook fan page to get members to my site and might plan to use facebook coupon to boost presence on facebook since it is not easy to bring members when the forum is still new.