Well, the ancient Egyptians and Greeks both had similar attitudes, and both ended up being assimilated by their conquerors, so it is possible given enough time. British rule only covered most of the Subcontinent for a hundred and fifty years or so, though, which isn't long enough.
Well, the is comparison does not seem accurate to me, and for several reasons so.
First of all, the communications (meaning both communication and transports) tools were much weaker in ancient times than they have been since modern times. And this technological gap does not work most people would spontaneously guess.
In fact, the most advanced the communications tool are and the easiest it is for a conquered/occupied cultural entity to resist cultural assimilation and to reinvent and reassert its old cultural identity. Just consider what effect the rotary printing produced in 19th century Europe. It halted most assimilation process that had been going on for centuries.
The irish, the catalans, the czech, the poles, ... etc, used it as a tool to escape from the assimilation process. Most people don't want to be assimilated and they only finally do so when they have absolutely no possibility to avoid assimilation.
You can see this trend having reached a further step with the development of satellite TV and high-speed internet. Assimilation of immigrants had become far difficult because immigrants from other cultural areas now have the possibility to live in their new country as if they still lived in the country they or their parents left. Children or even grandchildren of immigrants (who have totally assimilated themselves to their new country) even quite often decide that they feel more a member of the country from which their assimilated parents or grandparents originated than of the country where their assimilated parents or grandparents originated because they have the possibility to do so.
And by the way, the ancient greeks never were assimilated by the romans because they felt and were almost universally considered as culturally superior. It is in fact the roman elite that were assimilated by the greeks. And when the eastern roman empire began being run by culturally hellenic emperors, the eastern roman empire quickly became the byzantine/hellenic empire because the roman/latin varnish quickly disappeared.
And except for the urban populations that were a small minority of the whole populations, the egyptians never assimilated. Only a few decade after the muslim arabs conquered Egypt, the hellenic varnish quickly disappeared (although it took 6 to 7 centuries for Egypt to become in majority muslim).
So this brings US back to my previous statement. Britain lacked both the demographic advantage, the cultural advantage and the technological frame to assimilate the gigantic mass of indians).