It likely will not come out in court, the defense would need to do some magic to even not get it tossed out. To somehow link these past stupid kid remarks and such being dragged out on the net and link it to the shooting? Doubtful. Media is just trying to portray the kid in a bad light as if that somehow justifies the other side.
Being a juror once - I can tell you that whether it gets thrown out or not - it'll make an impression on the people who will matter most in this case. Its 100% character assassination - they're trying to prove he has a past history with aggressive and wreckless behavior - if his twitter posts were more outlandish and violent, I'd say they would be kept in court. But as it stands now, I agree with you.