There is a significant reason they ask for your address, its so they have you as a legal entity...
You can register using registerX or similar and get a recognised address to put in the whois, you register your names with the agency, they supply and address, and the registers know its not your address and know you are using an agency.
Some registers have lists of anonomous agencies that are approved, some dont.
With godaddy i think you can add it on after.
I put my hosts address in my public whois with there permission, and they forward any letters to me...