Yes - though the beach venue is at the Polynesian. You can book what is called a Memories Wedding, which is a small elopement style package for around $2,500. You can visit the Disney Fairytale Wedding website for the details, and I can't recommend the Disneyweddingpodcast.com more highly - Carrie has several episodes outlining Memories events.
If you want to get married on the beach in the same general area as Beach Club, you might want to look into a Swan wedding....I *think* they have a beach location?