It doesn't happen automatically. You would need to enable the "Custom DNS Record" option for their plan, and then add a custom A or CNAME record for the nameservers.
Should your nameserver IPs ever change, an A record would require manual updating, but it provides slightly better anonymity of hosting.
I have created an A Name in Clients Hshpere control panel pointing to the IP addresses for my Name Server.(yes the new ones: 204.x.x.x)
Unsing ns1.clientname.com and ns2.cleintname.com they ping back with the correct IP address, but when I try to use them in the Custom Name Server for Godaddy on a test domain of mine, I get a "unavailable error in field Host name1" and "name2".
Yes, you need to add them in domain hosts summary, a few tables BELOW nameservers.
After adding them, you need to set them in the nameservers, and it will work,note that sometimes it takes 1-2 hours before they will work, as domainhostssummary has to be updated in their systems.