Your account type can host multiple domains (2 -upgrade to get more). So the answer to your question is , yes you can add a domain to your account and setup a WordPress site with it. As per the link, you will need to add it as an Add-on Domain.
Hope that helps!
So it will be exactly as adding a newhost account as far as the visitors are concerned? They will get there with a new url just like a totally different website? No newname.oldurl.com? But just a www.newname.com? Thanks!
"if I add a domain, its really a subdomain but accessed by the new url just like the original site?"
When you add a domain to the account, it is considered a second website and is accessed just like any other website. Physically, the files are saved on the server UNDER your primary domain, so, yes, you can consider it a subdomain of the primary domain. However, as I said initially, the website is accessed as a separate website when you type in the URL in an internet browser.