Not only can you use a VPN to access The Pirate Bay, but you should use a VPN. The founders of The Pirate Bay strongly recommend using a VPN if you’re torrenting and using their site.
Torrenting creates a huge security hole, which, if left unchecked, can bring you a lot of trouble. First of all, it’s a security vulnerability that dramatically increases your chance to get hacked, especially if you’re using public trackers.
You can rest assured that your ISP knows everything about what you’re downloading and, in some cases, might even come after you. This is usually done in the form of a personal letter, which will often warn you about possible fines.