Does brain drain really affect a nation's growth trajectory? Take India as an example. India has been losing most of its bright minds to the west. India also ranks low in development. I would like to get a definitive answer to this cause-effect type question.

If India had somehow ensured that its talented people could not leave the country or If India had prevented its bright and ambitious minds from getting enticed and seduced by the west, would those bright minds have been forced to figure out how to improve India's infrastructure thereby resulting in India's development?

Or is it the other way, i.e., a nation's development is mostly (>80%) decided by the quality of its political leadership? The quality of Indian polity has been really bad since 1947. This is not a judgment but a plain fact. So is it that even if we had retained the bright ones they would have made no difference to India's future?

Could you give a data-intensive answer with stats? Do give intuitive arguments also to back it up.

My thesis is that a nation's polity decides the economic fate of the nation, not its talent pool because talent can be trained by the government of the day whenever it wants to. In India, people are not talented because they are born so talented but because competition forces that in the over-populated society. So my claim is that the fact that Indians have become so successful in the USA where they hold key policy-making positions should not be a cause of alarm. Had they been in India also, they could not have made any difference. And whenever the nation's polity improves, the nation will create any amount of required talent it requires just like monkeys can be trained any time you want them to perform in a circus.

Is my thesis wrong? I hear strong views on both sides and i cannot just make up my mind as to which side to follow. Please don't just give subjective answers/opinions (i know i have!). Provide some rigor and facts.
You have asked a very relevant question, and you must be new to economics or have not got a clue about economics of growth/development. And, you will not be able to get a 'definitive' answer to your question - it is not easy, and there is probably none! Should there be a definitive answer, we would not have to spend years doing PhD in economics.

There are plenty of resources which could give you a better grasp of the issue. 
For a start, read https://www.amazon.co.uk/Why-Nations-Fail-Origins-Prosperity/dp/1846684307