No, currently you must specify a domain name when signing up for web hosting services. You can either purchase a new domain name or use an existing domain name that you already own.
Note: If you sign up for an account using an existing domain name that you already own, it is up to you whether or not you will initiate the Name Server update for your domain name. We do provide a temporary ftp address so you can upload your files to the webserver and a temporary url to view your site.