A very important FAQ is does Google index Facebook comments written with the comments box on a website as part of this website?
The answer is YES, not only this, Google also treats content from the comments as a part of your site, you may get banned from Adsense because of Downloading urls in a Facebook comment, or my get penalized in Google search if you stuff keywords in a comment.
The only draw back of this is that Google index this content in Facebook comments some how slowly.
Yet Facebook comments are searchable content and gives you a SEO rise, in addition it saves space and bandwidth usage from your hosting payments !
Google has officially announced that its bot can crawl javascript content, however many webmasters do not relate this with Facebook comments.