Not really - I believe that when you do that with WordPress.com all you are doing is pointing the domain to the WordPress.com site.
You need to get domain and hosting (get it from the same place!) through someone like @dtbaker 's link, GoDaddy, BlueHost etc. then either use their hosting admin to install WP or download the files from www.wordpress.org and do it manually.
Once this is installed on your site then you will be able to install the theme you bought from here