I have and it works well, especially when sending links to articles/threads from the forum to the FB group as it brings traffic in from FB.
If you try to shut down all links to social media you'll eventually drive members to SM. If you keep the links open then your members will soon realise that your forum is part of your FB group, and vice versa. The won't have to choose between the two, or worse still leave your forum for someone elses FB group leaving you with just a hardcore group of members.
New members are the lifeblood of any forum without which your forum will eventually fade away and the tumbleweed will become evident.
Nope. I hate fb with a passion. I won't dumb down any of our boards by cross-posting to fb, nor do I want the typical fb members showing up at our sites. We used to have a page up but it was just another unattended mess that was ripe for abuse.