Is it possible to level doing pvp?
The 5v5 matches you enter in the Heart of the Mists (sPvP) will occasionally give you level-up tomes as rewards for playing in official matches.
The massive 3-way server vs server (WvW for world vs world) will give you experience for everything just like normal PvE, but you will die a lot as a low level. There is also a tournament starting this weekend so people might be a little more hostile than usual.