Donald Reaver
Donor
TBH, I think an out an out Japanese conquest of India is only really possible in the event of an out and out British collapse, with the Japanese moving in to fill the vacuum rather than invading in the face of coherent resistance.
And an out and out British collapse is perhaps not ASB but certainly a low probability outcome.
On the possibility of a defeat of the Chinese government freeing up troops. Well, yeah it would, but logistics... well, if we assume the war is similar to OTL and the yanks are in, then the Japanese would be rather reluctant to devote much of their navy to the Indian Ocean long term, meaning even the limited British forces devoted to the Indian Ocean IOTL will be adequate to prevent the large-scale use of sea transport. On land? Pushing over the Himalayas is totally insane and logistically unworkable; pushing up from Burma is better but still difficult.
Even with a British collapse, why would India welcome a new overlord. India has a strong enough internal government to resist any other external takeover.