You are correct, the Indian list shows Series 4 but Apple’s USA site does not. That tells us two things,
1. The same model is assigned for India and “rest of world” so a watch with the same model number purchased anywhere else in the region should be compatible at a technical level. However, that does not guarantee an imported device will be accepted by Airtel or Jio.
2. Apple India anticipates releasing within India soon, either as an unexpected addition to the first round or in the next round which will not be far behind. They have done exactly the same kind of staged deployment for the new phones with two groups a few weeks apart.
However, if you want to buy out of country you should purchase direct from Apple, not through a network or third party reseller who could lock the device to a specific network so it is useless when you get it back to India. Also, DO NOT buy from the Middle East countries like UAE, where we know Apple has been forced to disable apps like FaceTime on their products. There is no evidence yet how this will impact Watch functionality, but better safe than sorry.
My advice is to wait a few weeks, and check with Apple India when they plan to release. The advantage of buying locally is that you will be in your home area so the Apple 12 month limited warranty will be supported, and you will not be faced with carrying the watch back to UAE or Australia if you need to claim on warranty. If you buy abroad your warranty will only be valid in the country of purchase. You are also 100% sure it will be accepted by your local network.