Does brain drain really affect a nation's growth trajectory?
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