Apple Watch Series 3 (GPS + Cellular) is not locked to any specific carrier and has a built-in eSIM that copies information from the iPhone's SIM card.
The built-in cellular features require a carrier plan for your iPhone in the country of use that specifically includes support for Apple Watch, including your carrier activating the watch on the plan.
If buying Apple Watch Series 3 (GPS + Cellular) in another country, then you would need to buy a model that supports the relevant LTE and UMTS bands for your country and supported carrier.
There are three different regional versions of Apple Watch Series 3 (GPS + Cellular), each supporting different LTE and UMTS bands, as detailed here - Apple does not currently list any supported carriers in India:
Apple Watch - Carriers - Apple
I suggest that you contact your preferred carrier in your intended country of use to ask whether any given model of Apple Watch Series 3 (GPS + Cellular) would be compatible with any service plan that they may offer or plan to offer for iPhone and Apple Watch Series 3 (GPS + Cellular).
Note that the built-in cellular features cannot be used when roaming. Also keep in mind that warranty service availability may be restricted.
If used without activating the built-in cellular feature, then the Apple Watch could be used like a GPS-only model, using settings options that are localised for India.
The terms for Apple's Limited Warranty and for AppleCare+ when purchased in the US are detailed here:
You would need to contact Apple Support or an Apple Authorised Service Provider in India to establish whether service would be available in India under warranty or AppleCare+ for any given issue:
I'm afraid that no-one here can tell you what they would decide. You are not talking to Apple here - this is a user-based technical support community.