There are many people all over the world who ignore copyright infringement. There are people that know how to get around the safety measures put in place by the media companies and ISPs. They will use it and tell other people how. In other countries I'm sure the rules are not so strict and they will be allowed to download.
The Pirate Bay's Pirate browser I personally think it would not succeed because Google has always been a huge search engine website even though now a days people are using Fire fox. I personally feel that not so many people would go on the Pirate Bay's Pirate browser unless it is something that is "eye catching" and keeps people's attention while allowing them keep coming back.