Yes. There are a lot of people on twitter who harass, bully and send truly cruel things to celebrities. They are still people, after all -- if someone says something intended to hurt them it probably will.
Of course it is. That is why the comments in threads when people post stories about someone who was bullied, especially the one video about that female reporter talking about the man who told her she needed to lose weight, are laughable...it's like some of you do the same exact thing every day. Sales, chart positions, and superficial stuff like that is one thing...but people here take it too far. Of course it is bullying.