Purchasing a new domain name can be done in a matter of mintues with ease. However after you've bought your domain, DNS servers around the world need to update. This is called domain propagation. Before this happens you can still upload your site to a temporary URL with us and create your email accounts although they won't be working until propagation is complete.
Propagation can take up to 24 hours, however it's usually done much quicker in a matter of a few hours.