Will an iPhone bought in US work in India?

In general yes. US iPhones are unlocked and work with most carriers world wide.

Do note however, that iPhone 14 models sold in the US do not have a SIM card slot for a physical SIM card. They only support digital eSims which means for use in India, you will be limited to Reliance Jio as your carrier, as only they support eSim in India and only if they are willing to activate the foreign iPhone on their service.

Link-> Find wireless carriers and worldwide service providers that offer eSIM service - Apple Support

Also as mentioned by farm above, you will not have warranty in India and will need to physically return the iPhone to the US if you need any type of warranty repair.

You should buy the phone in the country where you plan to use it so that you will easily find a cellular provider. And the warranty is only good in the country where the phone was purchased. I just checked and I do see that there are Apple Stores in India, so you should probably purchase the phone there.

the only difference between iPhone sold in US and India is the SIM configuration, as Apple stops using physical Sim card in iPhone sold in USA starting from iPhone 14.

For sure, the price may vary in way make it beneficial for you to buy a phone from USA and use in India, but you can verify the specs using apple website in both countries to stay informed.

Let's assume you may plan to buy an iPhone 14. Here, you need to verify if cellular providers in India offer eSIM service as US-iPhone accept only eSIM. here 3 links for iPhone 14 tech spec page from Apple website in India, USA, and Canada:

1- Apple India: iPhone 14 Pro and 14 Pro Max - Technical Specifications - Apple (IN)

2- Apple USA: iPhone 14 and iPhone 14 Plus - Technical Specifications - Apple. ( dual eSIM only, No physical SIM)

3- Apple Canada: iPhone 14 and iPhone 14 Plus - Technical Specifications - Apple (CA) ( Same as India, dual sim accept one physical sim and one eSIM)

the nice fact here is Canadian iPhone is the same spec as iPhone offered in India, so you might buy from Canada and it will be typical for phones sold in India.