Face time in a middle east version of iPhone in India
I would not expect FaceTime to work if you unlock a phone purchased in Middle East.

https://support.apple.com/en-us/HT204042


FaceTime may be unavailable if your device originates from this country or region and becomes unlocked or is used in another country or region.

The footnote is very broadly worded. My presumption is that phones sold in the entire region have legal or contractual restrictions causing FaceTime to be bound to specific carriers and/or the device remain in specific geographical boundaries for FaceTime to operate or be blocked. It’s unlikely even if you export it closed box and do first activation in India that you would bypass UAE intended restrictions.  However, Apple did write this as a footnote, so I can’t say you’re out of luck across the board.
If you are uncertain when it’s time to spend your cash, be sure the return policy lets you test in India soon enough to return the device if you can’t be sure the features you need will work with the eventual carrier and eventual location. (Or be OK with whatever profit or loss you take reselling a “brand new phone” locally is acceptable risk)