Annexing Tibet is infeasible. Indian military is incapable of conquering and holding Tibet, let alone defending its own brder states and territories from PLA. Attempting to do so will widen the theater of war and PLA may very well wage full scale war especially if one of its largest provinces are invaded by Indian military as some here are trying to suggest.
India cannot militarily nor financially afford a long campaign war against China nor could India survive a long campaign war with China. Indian military may be able to make short term gains in such a conflict but in long term will capitulate and face a major defeat.
India keeps a sizable population, particularly the young ones of Haryana, Rajasthan, UP and Bihar for a reason. No matter how many they kill, India can keep sending soldiers again and again which China can't as its population is ageing.
Russians were able to invade Berlin because they had this advantage which Germany didn't.
This time, NATO will directly help India and use Indian soldiers to disfigure China just like how Indian soldiers were sent to conquer China during the Opium Wars.