I do not know what country you are trying to do this in, but in many countries, domain registration is done on paper. I can't say for sure about the United States, though.
I know at least in Italy, the process is this:
1. User visits registrar's website
2. User buys a domain
3. Registrar gets a notification that the user is trying to register that domain
4. Registrar sends a letter to Italy's domain registration service, who then electronically register the domain in the user's name.
I did a few Google searches about this and found no information. Maybe try calling GoDaddy customer service and asking them point blank... couldn't hurt, right?