The short answer here is that Google loves to crawl and index active forums that are always pushing out new and unique content. So adding a forum to your site could definitely bring in some traffic if your forum is SEO friendly. You will want to push out sitemap updates regularly so search engines can find these new posts/threads easily. You will also want to do some brand awareness of your main site on your forum. Because the new traffic that comes will be at your forum and not your main site. So making sure these visitors can find your main site from your forum is critical if you are trying to boost activity on your main site.