I just added a Facebook page_id meta tag to the homepage of one of my sites that I also setup a Faceobok page for last week to play with something else, ("#######..." is the id of the facebook Page I setup).
Fantastic CTR isn't it. And that's from presumably genuine "likers"; you'd expect it to far out-perform paid ads. What a waste of time.
I don't understand the connection between a "website page" (domain root with OG mark-up and accompanying like button and "admin page") and "fan page"... I made a fan page, which is publicly viewable, then the website itself like buttons made an "admin page" which looks exactly like a fan page but doesn't seem to be publicly accessible. Since the fan page is just the front for the website on Facebook, it seems to be they should be merged so that likes on the one count for the other.
I thought that's what the page-id property was for but adding it didn't change anything for me, the new 'admin page' that looks like a fan page is still not publicly viewable. Bizarre. I suppose with the pathetic click-thru results it's not worth wasting time on.