As noted on your question about Twitter, Facebook also uses rel=“nofollow” on links, so having links out to your home site from there won’t do anything for search engines, although it will refer real humans to your main site, which is certainly useful. Provided people are making their way to your Facebook page by some means. If people can’t interact with you and leave comments, what would be the value for them on the Facebook page to begin with?
Google likes blogs. Create (at least) one blog (with regularly added content) and disable the comments. That’ll do more for you than a Facebook group. Or put a link on your Facebook page to your blog, that’ll hopefully get real prospects reading it.
Has someone told you a Facebook page would increase search engine crawls or rankings of your main site? It won’t. Sounds like you may need a new SEO advisor.