in OTL the Viceroy was quite worried about the effects of pronouncements from the Caliph upon Indian (and Persian) Muslims. I tend to think that the effect of this will be to exacerbate the Hindu/Muslim divide even worse than OTL, and with the British authorities appeasing the Hindus out of fear of the Muslims being subject to the Sultan, who is in turn subject to the Kaiser.
I suspect that something like OTL will be the eventual result, but probably bloodier - the princely states will be seen as stooges of the British in crushing any opportunistic rebellions that might break out after the Great War is lost, and the Muslims are likely to be even more nationalistic for the reasons above. So probably one Hindu India and one or two Muslim Pakistans, probably with different names. I don't see balkanisation because the source for that was the princely states, which would have even less influence in TTL if the independence types got their way.
OTOH if you want to be optimistic, you could say that any postwar British government wants to dump all the problems India is foisting on it and thus fast-tracks it for one of the dominion plans as implemented in EdT's timeline for instance - but these are liable to be so rushed that they might implode in the long run.
Very interesting analysis. However, I personally tend to think that in this scenario we might see a closer cooperation between muslims and Hindus, a unified "India" and no Pakistan or analogous muslim independent state.
IOTL, the "traditional" position of Indian Muslim from late XIX to the first decades of the XX century was, I think, to be
against both independence and any form of self-gorvenment. They had adopted this view because they considered than in a democratic and/or independent India they would be subjected to the will of the mayority (=Hindus). That's why Muslim leaders were against even some of the least radical proposals of Hindu leaders, like increasing the number of Indians in the Administration or granting autonmomy at a local village-level. They did so because they realised that those who would benefit from these meassures would be mostly Hindus, and that this would lead to Muslims being rulled by Hindus (the exact opposite of what had usually been the rule in India from the XI century onwards). This fear was the reason why several Muslims leaders prefered to be governed by
British members of the Indian Civil service than to live in an independent country ruled by Hindus.
The British used the Muslims card on several occasions, whenever the Hindu- dominated Indian Congressed seemed to be demanding what they considered was too much for the time. They did so around 1890, and they did it during the 30s, if I'm not mistaken.
However, there was a brief period when the British weren't fully able to play this card: from around 1900 to 1924. Why? Because during this period the British had abandoned their policy of protecting the integrity of the Ottoman empire and had adopted what was percieved as an Anti-Ottoman policy (due to the fact that the Ottomans were now under the German orbit). The Caliph exerted a strong influence on Indian Muslims, and encouraged them to rebelled against the British (specially during the Great War). Indian Muslims, meanwhile, weren't happy to be under the ruled of a government against whom the Caliph had declared a holy war.
Gradually, Indian Muslims, who used to be against the Independence for the reasons stated above, began to view it with more favourable eyes. The Indian Congress, who had started the fight earlier, seeking nothing more than greater participation of Indians in the government (at first), was happy (and surprised!) with this change of attitude among Muslims. Hindu Congress leaders were now surprised to see that Muslims, once so against all kind of modification of the status quo, were now more radical than they were. Muslim and Hindus got toghether and pushed foward in order to get concessions from the British. Leaders like Nehru were happy to use the Muslims resenment (against the British policy towards the Caliphate) for their own needs. Muslims and Hindius began to see themselves as being part of an "Indian" nation (this was favoured by the fact that congress leaders, though Hindus, were pushing for a secular Indian state). More Muslim leaders joined the Congress.
However, IOTL, this union between Muslims and Hindus stopped when the Caliphate was dissolved. Muslims began to fear the Hindus more than what they hated the British for what they were doing to the Caliph... because the said Caliph didn't exist any more. The British were then again able to play the "Muslim card" againt the Congress.
So, if the CP had won, and the Caliphate had survived, Indian Muslims would continue to look foward for independence, regarless their fears of ending up in an Hindu-dominatet state. They would prefered that than being under the rule of a government that was and would remain hostile to the Caliphate.
I know Hindus were gradualist in OTL, but in this TL, with Muslims wanting independence, Hindus woldn't want to stay behind. There will be strikes, boycots, and even terrotrists and guerrilla actions. A coordinated strategy would need to be in place, so we might see more Muslims entering the Congress (or the secret organisation that would replace it if it's made illegal by the British) Unable to play the Muslims card, the British might try to play the "princely state" card. But, unlike the "muslim" card, this is a much weaker card. People tend to be passionate about their religion or their nationality, but i don't see the population of this states willing to die to avoid their incorporation in the Indian Union.
We might see a long and bloody fight between "Indians" (both Hindu and Muslims) against a British government who has just lost a great war and won't be willing to renounce easily to the sole possetion that grants her her status as an "empire". Boycots, strike, mutinies, terrorism and even guerrilla actions will be common. When the independence is finally ahieved (with German, Russian/Soviet, Japanese or American help) a trully united India will come into being.
Ethnic and/or religuos conflicts will appear, but in a distant future (let's say, in the late 1970s if independence is achieved in the 1930s). Before that date, the sense of brotherhood that would have been formed between muslims and Hindus during the long struggle for independence will be strong enough to stop this tensions from manifesting themselves. The secular ideology of the Congress might also help a lot in this sense.