That's correct. Once you sign up with us and receive the Welcome Email, you can change the DNS to our server. And f you coordinate the taking down of the site from the old host and moving to our servers, you should incur little to no downtime.
Emails on the other hand are a little tricky. As the DNS changes bounce around the net, you may lose a few emails here and there, but overall you shouldn't lose anything significant in the move. Just maintain access to both sites until the transfer is completed to be sure.
I'm very glad to hear you are going to be using our services
