How well have they succeeded? Pretty well when it comes to contradicting existing laws and setting a new and bizarre precedent.
Not so well when it comes to actually stopping The Pirate Bay:

Much like the use of heavy artillery would cause a lot of damage without necessarily hitting the duck, it took The Pirate Bay only a few hours to get online again, and yet a few hours for DNS-servers around the world to get up to date with their new IP-addresses. A minor inconvenience. However, the damage inflicted on the free Internet in Sweden by Stockholm tingsrätt and that damn mafiaa may very well be irreparable. Good job, you absolute morons.