Well that all depends. First most requests don't go to the root servers -- they are far too important, second there is caching on the isps servers. To have any effect other than to make sys admins dehydrate anon have to keep the attack up long enough to have the caches empty (if they are indeed configured to flush even if they cannot connect to the root. They may not) and there are several layer deep caching (your isp is but one. Your local computer may also have one).

But assuming they can keep it running long enough for the DNS service to die(and they may very well, that flaw is pretty smart though they have to use the actual ip of the vulnerable DNS servers, which means that it can be filtered if the admins are smart enough)? Well goodbye internet -- you would just get an error, no matter which website you would try to access. A pretty grim situation, but not likely.