no sir. The beta is not to test in game content, as they have been doing that internally for almost 2 years. The beta is almost solely for their servers. As such, they won't add anything new =P Which of course isn't bad imo, I want as much fresh as possible.
Right after Skeleton King you find out what actually is the fallen star, which would be too spoilerish, so no more quests in beta. I doubt they would add new ones even if it wasnt spoiler, they just want to release the game.