This actually happens all the time, though you may not realize it. Say you buy a domain from a registrar, then build your site on a web host that uses that domain name and gives you a unique IP address. You go to the registrar's site and change the DNS to point to the new site. You can use the site via just the IP address all you want before changing the DNS, you just can't get there using the domain name until you do.
I've done this before when moving a client's site from one host to another using the same domain name. Let's say the domain is called "yourdomain.com." You just create a new account on GoDaddy with the same domain "yourdomain.com" and develop the WordPress site using the IP address for the new account, then when you have it all working, change the DNS on the boss's account to point to the new site, then go through and change WordPress to use the domain name instead of the IP address.
The other thing you can do is call GoDaddy and tell them you want to transfer the domain and the hosting (if they have it) to your account. They will help you do it, and it will be nearly seamless. Then, develop your new WordPress site in a subfolder on the new domain/account. Once you have it the way you want it, move/rename the root folder containing the old site and move the WordPress installation into the root directory.