I belong to some Etsy groups on FB. I'm active on about two of them.
I promote every so often on them. The one i'm more active on is similar to this team, so I'll help every so often when people ask questions.
I really don't promote my FB page on those teams because it ends up people liking my page just for likes on theirs and I get bombarded with messages saying ,"Hey, from XYZ team. I liked your pages, come like mine." Just as a personal policy, I only really "like" pages and/or items that I really like. Begging, and those games, really irritate me.
But the more you post on your fb page (well on all social media), the more followers you will get. But you have to make sure its interesting things, not just promoting your store. People will get turned off and just see it as spam.