Indian nationalism is only half the issue here. More to the point is the issue of regionalism in decision-making. Sure, you might be able to divide up India so that the Tamils feel like they have nothing in common with the Sikhs or the Gujarati or the Mughals or I don't know who, but if you have issues which affect the subcontinent enough then those different regional identities will vote together to counter-act British "better judgement", even if they don't realise that that is what they are doing.
Take for example a world where the Imperial Federation has come about. It's the year 1950, there has been only one world war, and Big Bad Democratic Russia is power-playing in Afghanistan. Now, in London the Diplomatic Corps believe that they have things in hand. India is half a world away, so they believe they have the time to build covert alliances with the rebel Afghani factions, Baluchistanis and such and they plan to use this to persuade the Russians to back down on their threats of cutting supplies to north-west India unless it cedes them some land. Let's pretend for the purposes of this scenario that London genuinely knows what they are doing, and Moscow privately believes that they are only posturing to force concessions out of London.
Skip now to India. The MPs on the border are very nervous. They can see the Russian garrisons along the border and they know that their lands will be the first to get obliterated if there is a war between the two. However, they also know that Russia is having a bit of a spat with Austria and France, its two European allies, and they are unlikely to want to enter a war with the Federation over Russian expansionist plans. Privately, the feeling is strong that a pre-emptive strike could turn the war their way fast. The border MPs bring a bill to the table proposing a declaration of war against Russia. All of the white MPs vote against. However, India is used to feeling threatened by Russia. 80% of the Indian MPs vote in favour. The Indians carry the vote all by themselves, and London's strategy and planning goes down the pan as the vast weight of Indian voters forces a war that they had planned to avoid all along.
Or to hypothesise another (shorter) scenario. It's 1950 again, and some of the white ex-colonies have started toying with the idea of universal healthcare. India still exists largely in squalor, the rate of doctors to citizens is ten times higher than in the white countries, hospitals are disease-ridden and underfunded. The Indians want any sort of upturn in their living conditions, as they feel that, as part of the same country as Britain, Canada, Australia etc, that they have the right to equal standards of living - and they are probably right. A bold Indian back-bencher proposes that the entire Federation institute a National Health Service which will be able to provide at least basic levels of healthcare for a very low insurance payment if not free, using a slice of the government's budget. India unites in its desire to improve the standards of living across the subcontinent. The white MPs either vote in favour on lines of conscience, or vote against on the grounds that the Federation cannot afford to institute these plans as it will bleed money away from the white states and actually decrease standards of living there as the disparity is so vast. It doesn't really matter how they vote, however, as the Indian vote is enough to completely overrule any organised vote against.
It's these kind of scenarios that I think make this a dud proposal. At the end of the day you can make the various areas of India hate each other, but if a bill comes up which stands to benefit India in general, the Indians will still bloc vote in favour and completely negate the white votes.