True, it's very likely we wouldn't have a Buddhist majority today. I suspect this could also have significantly altered the history of Judaism. The Alexandria community was a powerful influence in the pre-cataclysm days while Jerusalem would have lost much of its prestige if this instance of 'divine intervention' hadn't come about. In those terms, a Roman world would likely be much friendlier and kinder, without the heretic-hunts and powermongering of the Buddhist sects and the prickly Judaean temper. From what we know of the Roman religious tradition, it was a lot like the Hihonese, willing to adopt outside influzences and accommodate different practices.
The political fallout is harder to gauge. I disagree that the Empire had much of a survival chance. Despite the universal propaganda we find celebrating Caesar Augustus, he was nothing more than a successful strongman, another Pompey Magnus or Caius Julius Caesar. It is more than likely his power structure, cobbled together as it was, would not have survived the first succession crisis. Yet without the impact, Roman civilisation would likely have continued to exert a centripetal force and we would have seen much more unity around the Mediterranean. Who knows, they might have brought the Celts and Germans into their ambit - militarily, as far as we know, they had already begun the process. Something like sub-Roman Gaul and Spain could have prevailed all over Western Europe.