If you can run javascript on facebook page then yes, if not then no. It won't be something in adsense rules but rather in facebook rules.
i dont think you can do . its not mentioned in adsense policies about facebook page but it may get your account disabled. you can try to get traffic from facebook page to your website thats best for you. the second thing you can not run java script in to facebook page.you can just put links and photos .
If you think you can do it, care to share how? I don't know if it's possible to put iframe on facebook, but anyway that would be against AdSense TOS. But if you can put javascript somewhere on your facebook page, then adsense can be shown on it, because you don't have to own a website in order to put adsense on it, ie. adsense sharing sites and blog platforms.. It's only a matter of facebook allowing javascript or not, I think allowing javascript is foolish for security reasons, so it's unlikely they allow it, but since they know javascript 100000 times better than me, maybe they have it sorted out, me I don't allow javascript or restrict a lot fo html on my multi-users sites out of security concerns, I prefer to block most of things except for plain text, and even then I don't feel secure.