Have you tried promoting the Facebook page with facebook advertising? It works really well and can get some extremely targeted visitors.
There is no restriction for facebook pages in AdWords. Btw, I think facebook ads should be more effective for facebook page promotion.
While there are no restrictions on promoting Facebook on adwords I have to agree with everyone else that most likely the ad will do better using FB advertising and also IMHO FB seems to like clients who use their ads to move traffic around there on site.
Yes in fact FB advertising can convert pretty well by targeting the right demographics. It might convert better than Google so why bother?
its better use advert of facebook than google adwords for this case. cause we can target more accurate and the cost when compared to google adwords is a little bit low. so, i'll go for Facebook advert than google adwords for this case.
I must agree, you would be able to get the most out of it should you be placing it to facebook advertising. Those who will try to visit your page will surely be that person who had the most interest with your product, site or content.