You are right that the CELTA will be recognised worldwide, regardless of whether you take it in India or Turkey. The advantage of taking it in the country where you want to teach is, as you thought, the possibility of developing local contacts, often through the CELTA course centre itself.
All employers have certain criteria when it comes to recruiting teachers, so having those local contacts will be of benefit only if you meet the other criteria that the local employer is looking for.
Legislation in some countries, for example, only allows work permits for certain nationalities.
In terms of not being a native speaker, your employment options will, unfortuantely, be more limited. Students in many schools demand to be taught by native speakers, and of course the schools have to meet this demand to stay in business. Thankfully, this is beginning to change, as people realise that you do not have to be a native speaker to teach a language effectively! But the change is slow, and so you will have to take this into account.
So my advice is to research thoroughly the opportunities for non-native speakers in the country where you would like to teach (check jobs boards on this site and others to get an idea of typical requirements), and also to check that there is no issue with work permits for Indian citizens.
I hope this helps.