An Indo-China war would solve the overpopulation problem in a couple of hours (of mutual nuke exchange). For humans, it would be the Toba Bottleneck Part Deux.
Unfortunately, China would probably come out ahead in an exchange. China’s got somewhat more than twice as many weapons as India, and has aircraft to deliver them. India’s all have to travel by missile.
In any event, neither would be likely to go all the way to MAD, since there’s no benefit to either. A ground conflict is the more likely scenario, only bringing in nukes as denial weapons. The dispute between China and India is land. China holds a few small snippets of (really really) worthless barren moonscape up in the Leh/Ladakh area north of Kashmir that India wants back. At the same time, China would really like to snip off a good chunk of the Arunachal Pradesh region of India (and maybe everything on that side of Bangladesh). It’s hard to get any benefit from “taking” an area of land that glows at night and can’t be inhabited for a few thousand years. I know China plays the long game, but that’s probably a little too long even for them.
Now, Pakistan, on the other hand, just might be insane enough to try for MAD.