In my opinion, merely recognizing Tibet as a sperate country will only going to be seen as a Policy change on India's part by China and at the same time, it doesn't translate into negating China's claim on AP as a part of Tibet and more so won't be enough to stop Chinese atrocities on Tibetens in Tibet. We should not forget India's intentions to free tibet from the clutches of China during 1950 and subsequent warning by china to have war only reinforces the fact that China always supports its vested territorial claims backed by its Powerful Military, as China always use contemprory Geo-Political scenario into equation while making any major move to achieve considerable part of its territorial claim. Testimony to this fact is Soviet support to china during Korean War and unwillingness of major power around the world to support Tibeten cause and protect them from Chinese invasion, as they were engaged in major rebuilding process to recover from the afteraffects of World War-II.
Another major aptitude of China is think long term and accordingly craft all its stretegies around it, which steam from the fact that it willing to create every possible barriar to all emerging nations around it to have some sort of a issues and to force them deal with by spending considerable time and money. Exactly this is the reason why China is using AP to play with India to create unnecessary controversis to deal with.
We Indians, instead of straight away bringing in Tibet into the picture, we first need to aggressively bring India's own territories which have been forceibly occupied by both Pak and China in the form of POK and Aksai Chin. Unless we pursue this two long standing overdues, till then it will be foolish to play Tibeten card to our advantage. We first need occupy our lost territory of Kashmir from Pak by declaring War, no matter what price we need to pay for it even at the cost of economic rebuilding. Unless, we don't willing to sacrifice something major, till then we cannot expect nations around us from stop claiming India's legal territory and create challange for India's Integrity.
Always remember China's recent intrusion and in one case writing on rocks with paint something in Chinese language which had a particuler meaning. And that meaning according to Indian Elits on Chinese matter is that China's Cultural expansion simply doesn't respect any boundaries and barriars, for which Chinese will everything it can to comply with such expansion.