Torchlight 2 Reactivation

Since Torchlight II will have completely new character classes, and none of the ones from Torchlight I will have a comingback, you will not be able to use old characters.

It is also stated in Torchlight II FAQ in Runic Games official Forum:

Will I be able to import my old characters?
No, the original characters will be in the game as NPCs, as will other NPCs of the Destroyer, Vanquisher, and Alchemist class types. Additionally, due to various changes in gamplay systems the old character files will not be able to be imported as-is, as detailed below:

Along with the story the game will use a new wardrobing system opposed to the one in Torchlight. As a result they did not reuse the Torchlight character assets.

While T2 is definitely a direct sequel of T1, you have to realize, these are both games that focus on "kill everything that moves" and "loot everything you see". The storyline is only there to help players become familiar with areas and the enemies that arise from them, but isn't necessary play T1 over T2.

Honestly though, T2 is a completely reworked version of T1 that features a whole slew of new improvements, as well as dedicated modding support, etc.

Consider this, it's very much like the L4D series. While L4D had a storyline, and so did L4D2, the story lines were only vaguely connected, but the game was more about a zombie co-op game. This isn't to say the storyline was non-existent, but it's there to guide players to understand what's happening around them. Gameplay-wise, much like TL2, L4D2 is a very very nice upgrade to L4D, in that there are more weapons, more game modes, more special infected, and other nice sweets.

Basically, consider T2 over T1 as a nice upgrade, with more features than its predecessor. If you really really care about storyline, by all means, it doesn't hurt to play T1. If you really like gameplay, then I'd say it really doesn't matter.