Wont work, most people do not use the root servers.
The non root servers cache DNS records from the DNS servers so the only harm taking out the root servers will do is stop people from getting the correct IP for a website if they were to change their IP address.
For example, if you are using your ISP's DNS server and anon takes out the root servers. Google.com will still take you to google, but if google for some reason decided to change their IP address during the attack, then you would have trouble accessing it.
The access to the DNS servers are also based on location so the attack will have to be carried out on all 13 servers from 13 different locations that are close to the servers.
Not to mention that each of the 13 roots are massive server farms with a connection with a massive throughput. Their attack will be the equivalent of taking down google 13 times.
Remember the 13 root servers are responsible for updating the DNS records for the entire internet
To take down the 1 servers, you will need to get like half of the Internet attacking those servers.