I think you should be able to, as long as you’re willing to purchase a new domain. I own a couple of old domains which redirect to my blog; if you register a new domain and then give it time to redirect properly, it should work, but nobody is going to know the domain exists, so it wouldn’t have much effect. If you bought it and then went to Dashboard > Options > Domains and put the blog at the new address, that might make more sense; people coming from your known old address would reach the new one. But what that would mean for your Technorati ranking, etc., I’m not sure; you’d probably be starting all over again. http://faq.wordpress.com/2006/11/10/domain-mapping/
Were you wondering if you could pay $10 per year for both domains? They limit it only one domain… either if it’s simply domain.com or blog.domain.com. I have submitted a change request from domain.com to blog.domain.com.