If you didn't know, India and China HAVE fought a war in that region, and you always fight wars 'at the end of supply lines' by definition, so not sure what you mean by that. In fact, both countries have the ability to fight extended wars. India has been fighting a war for decades on its western frontier with Pakistan which is as rugged as the eastern frontier with China. India maintains the highest battleground presence in the world on the Siachen Glacier. So no, the prospect of a land battle on the Indo-China border is neither unlikely, nor unprecedented.

That said, modern China is a pragmatic country whose primary focus is to keep its own population happy. China has a lot of hurdles in the path to the realization of that goal, and needs the economy of the region to stay stable for that. If China attacks India (or vice versa), global supply chains and economies will get severly affected and in turn will have an avalanche effect on the economies of both the countries. Hence, practically speaking, neither countries would wage war on each other unless taken over by a whimsical, dicatatorial leader (and which dictator isn't whimsical?).