“In theory, yes. However, the main servers the gov is likely to go after are the top-level domain controllers.”
These are called “root servers” They serve at the root of the DNS (domain name service) tree. There are around a dozen root server sites in the US and more are distributed around the planet. DNS is much like a phone book. One looks up a name like freerepbulic.com and DNS returns the IP address of the server(s) associated with the domain. You can see where some of the root servers are located by going to http://www.root-servers.org/ . Take away the root servers and really bad things happen to the internet.
For a very good video on how the internet and TCP/IP works, go to http://warriorsofthe.net/ . This video is standard viewing in the first Cisco CCNA course.
Actually, I already have a CCNA (though I never saw any video when I was studying for it, and I need to renew), as well as an MCSE, a MCSA, and a CISSP. And I have a Masters in information assurance, but I’m sure there are plenty of folks for whom this is useful.