I opened my GoDaddy account and bought a domain 2 days ago without the privacy option. Since then I've received 22 spam emails and 5 telemarketing calls for web design, hosting, etc. I knew some info would be public, but this is just ridiculous. Probably too late to go back and hide that info huh?
It's pretty shady to have to pay to not get dozens of emails and phone calls/day...
This is common with any domain registration. Those calling you aren't associated with Godaddy. They stop after a while if you ignore them. Mine isn't locked down and I very rarely get calls anymore.
Another fix you could use, is register with Google Voice and get a phone number from them and use that went setting up domains. That way, when people call that number you will know it's probably a telemarketer.