Yes, you can promote anything you want over facebook. Before you promote your services. First, try to add good value to your posts and make yourself seen as a helpful person or the expert in a specific niche.
If you treat your Facebook fan page as a forum or gathering spot, you are more likely to cultivate a community spirit among your blog readers. The blog readers could give feed back on your latest blog posts or contribute content to the page that could later be featured on your blog. You could post frequently asked questions from readers along with answers or have a Q&A where you pose questions to your Facebook fans and have them answer the 'question of the day'. Just a few ways to use your Facebook page for your blog.
You can promote your blog on facebook but facebook can't help to boost your SEO. facebook just give you traffic.