if I purchase Apple watch series 3 or 4 (GPS only) from USA, will it work in India? I am going to USA for 15 days next month. I am thinking to buy an Apple watch series 3 or 4 only GPS, no requirement for cellular for me. Will it work when I come back to India? I am living in India permanently.
The Watch will function perfectly fine in India, however some functionalities will not work or be limited. This is for example the ECG feature, turn-by-turn navigation, the News app, etc.

There's no reason to buy the Watch in the US in hope of getting access to US-only functionality, as that functionality most probably will not be available in India and will cease to function when you get back, or at a later time when the software is updated.

You enquire about the GPS - it will work fine all over the world. Also in India. Other answers here focus on other positioning systems such as the Indian IRNSS (NAVIC). It is not supported on the Apple Watch, no matter if you buy the watch in India or in the US. It is also not supported on iPhones or any other Apple device. The Apple Watch supports GPS (US operated), GLONASS (Russian operated), Galileo (EU operated) and QZSS (Japan operated).

As you're looking at the model without cellular, you do not have to worry about cell coverage. The other answers that talk about LTE bands, etc. are irrelevant when the watch does not have cellular. The Watch will use your iPhone for calls, SMS, etc. and automatically supports whatever iPhone you have with the LTE bands, etc. it is using for communication.

The last thing to note is that the Watch in the US comes with a US charger. I.e. they are 110V/60Hz and a different type of plug, compared to the 230V/50Hz system and plugs used in India. You will need an adapter to be able to use the charger, or you could substitute any ordinary USB charger. The magnetic charging puck for the Apple Watch comes as a seperate cable that is plugged into the charger, so you will be able to use a different charger very easily.