that worked nowhere in the medieval era. The Vikings, the Arabs, the Mongol Raiders, the Nippon pirates etc all showed that centralized religion meant nothing in front of politics. Also Hinduism varies in India from place to place. So will this Buddhist India. Just like how in the early days, Catholics denounced Orthodox and Protestants, there is no saying this kind of things won't happen within India as well.If India was Completely Buddhist, there is a good chance that Religious Identity will become more pronounced and they will band together against external invasion, especially if its against their religion
Some Southern King will say ' The northern version of buddhism is heresy, why should i support them' and everything will go down the drain. it's like how Indochinese and Chinese buddhists look at each other with suspicion and distrust but much more pronounced because of geopolitics.