According to the Chief Rabbinate of Israel…surprisingly yes. A somewhat shockingly unanimous decision was made 2 days ago by the religious government body that brainstem death constitutes death according to Jewish law. This would make it halachically permissible to remove an organ from a braindead person before the heart has stopped beating, making organ transplant possible. Their ruling did not have to do directly with organ transplant, but it definitely sets the stage for it. Together with modern organizations such as HODS, the Halachic Organ Donor Society, we may see Israel soon, and Jews in general more willing to donate organs to those in need.
The bill approved by the Rabbinate, recently passed by the Knesset, has even more far-reaching consequences. For one, it would allow disconnecting a braindead person from life support even if his heart is still beating. It would also allow a woman whose husband has suffered braindeath to remarry.
This reverses a 30 year old decision that halachic death only occurs at clinical death, leading to many legal complications with regard to all of these issues. Though the decision was never implemented for technical reasons, the shift is still dramatic.
The only influential Rabbi disagreeing with this decision is Yosef Elyashiv, long known as a staunch conservative and leader of the Lithuanian sects of Ultra Orthodoxy. He holds that no organs may ever be removed under any circumstances. But he was overruled.
As of today, less than half of the families of braindead patients agree to donate their organs, 35% for religious reasons, and the rest for personal reasons. Altogether, almost 58% refuse to donate organs. That figure could begin to lighten now.