Sweet idea!
I love the idea. The India-Pakistan split is a fault line that threatens more than just its South Asian neighbors causing needless suffering IOTL.
However, I'm afraid we're making a space-filling empire here if we include Burma.
I'm completely aboard with how the Karen and other non-Burman groups in Burma would love having a counterweight to Burman domination by all being little fish in the Indian sea, but the centrifugal pressures would be tough to manage for India.
Plus, India has a long tradition of letting the local bosses handle things without a lot of supervision.
So iI argue that in this case, the non-Burmese minorities 'd be even more marginalized and exploited in Indian-absorbed Burma, when the Burmese could call in federal reinforcements.
Not impossible, mind you, just IIRC, the Burmese wanted independence for themselves and weren't part of the INC.
You'd need a lot more proselytization and collaboration between Indian and Burmese activists from 1930 on. IMO, it's much more likely Burma and India having a free-trade agreement, customs union, and so forth but allowing Burma to be a friendly neighbor ruling itself rather than a headache to rule from Delhi.
Also, I like the idea of India and the US getting together on a platform of de-colonialization and so forth, butterflying away the Vietnam War. A tasty development there, avoiding the myriad casualties thereof.