As you said you will buy an unlocked iPhone 7, which means you will pay the full price. It will definitely work in India. T-Mobile iPhone just means it will come with a T-Mobile sim card. read more
T-Mobile does work on GSM which means you can use it on not just Airtel but also Vodafone and Idea networks. This goes the same for AT&T as well. But Verizon and Sprint configured iPhone 7 does not work on GSM, it works on CDMA. read more
I'm in Bangalore India now with iphone 6s plus with IOS 10.2.1 and T-Mobile Carrier version 27.2. I am happy to report that I was able to get service running with a tiny bit of work as shown below: The default carrier I was able to roam onto was Vodafone IN. The phone should go to Vodafone when you power on. read more