I very highly doubt it, unless the prosecuting attorney asks a question that opens the door for it. The only part of Martin's character that appears relevant to me as a legal matter may be whether he had a tendency to violence of the type in Zimmerman's account of the night. Whether or not Martin was really acting suspiciously doesn't aid Zimmerman when the charge is that he was 'depraved' with respect to strangers in the neighborhood who looked suspicious, obsessively concerned that they may be committing crimes and that they always got away, following Martin, allegedly confronting Martin, and so on.
People can yell "it's relevant." Yes, to them, but not to a court. In my opinion, in a courtroom it's not just that it would be considered more prejudicial than probative. It just wouldn't be considered relevant. The relevant character trait of Martin would be whether he's prone to violence, not whether he's prone to theft.
No. There's no way it's coming in. As I understand it, Martin wasn't accused of stealing jewelry and he wasn't charged with stealing jewelry (I don't even know that it was established that the jewelry was stolen). It would be irrelevant if it existed, but there's no stolen jewelery charge against Martin to be admissible.