No. The reason we purchase domain mapping is because it creates a seamless redirect form the original blog URLs to the same content under the domain URLs no matter where they are clicked anywhere on the internet. In other words - don't sweat this. The blog is going to be hosted exactly where it is now and all the changes is the URLs.
In order to map to a domain one must have an underlying .wordpress.com subdomain blog to map from http://en.support.wordpress.com/register-a-blog/ and the domain name you desire must be available for purchase, or you must already own the domain URL.
After you have registered a .wordpress.com blog you log in as Admin under the exact same username account that registered the blog and purchase a domain name by purchasing an annually renewable domain mapping upgrade for the blog from the blog's dashboard at > Store > My Upgrades.
See here if you do not own a domain http://en.support.wordpress.com/domains/
See here for mapping an existing domain that you already own http://en.support.wordpress.com/domains/map-existing-domain/
See here for mapping a sub-domain (for a domain with an existing website) to your WordPress.com blog http://en.support.wordpress.com/domains/map-subdomain/
Dashboard > Store > My Upgrades is where you do the primary blog set up knowing it can take between 24 - 72 hours for domain name propagation to take place throughout the internet. You can view the DNS changes here > http://www.whatsmydns.net/ What's important during that stage is to be patient.