I think this is more about them than a genuine protest. All it will do if it does work is show their might: I can’t see how it will effect meaningful change of any kind.
Will it work? It depends on how many recruits they get (real or virtual). I suspect they will disrupt some of the root servers, but I think the root server clusters will be able to handle it overall.
Other than the lulz, I don’t see this working out well for Anonymous. The perception of them may shift from We-Take-On-The-Big-Bad-Organizations to We-Are-Reckless-Vandals. They already took a hit when they backed off from taking on Mexican crime lords. This may result in them taking a further hit. But I am hedging here, obviously….we shall see the result soon enough.
For some details on this, see Pastebin.com